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Longer titles found: Standard probability space (view), Gaussian probability space (view)

searching for Probability space 105 found (318 total)

Pitman–Yor process (440 words) [view diff] exact match in snippet view article find links to article

parameter, a strength parameter θ > −d and a base distribution G0 over a probability space X. When d = 0, it becomes the Dirichlet process. The discount parameter

Markov kernel (2,052 words) [view diff] exact match in snippet view article find links to article

defined by Lawvere, the category of Markov kernels. A composition of a probability space ( X , A , P X ) {\displaystyle (X,{\mathcal {A}},P_{X})} and a probability

Stopping time (1,938 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \tau } be a random variable, which is defined on the filtered probability space ( Ω , F , ( F n ) n ∈ N , P ) {\displaystyle (\Omega ,{\mathcal {F}}

Snell envelope (404 words) [view diff] exact match in snippet view article find links to article

Snell envelope is named after James Laurie Snell. Given a filtered probability space ( Ω , F , ( F t ) t ∈ [ 0 , T ] , P ) {\displaystyle (\Omega ,{\mathcal

Predictable process (272 words) [view diff] exact match in snippet view article find links to article

left-continuous processes.[clarification needed] Given a filtered probability space ( Ω , F , ( F n ) n ∈ N , P ) {\displaystyle (\Omega ,{\mathcal {F}}

Probability Sun (667 words) [view diff] case mismatch in snippet view article find links to article

her 2000 publication Probability Moon. It was followed in 2002 by Probability Space, which won the John W. Campbell Memorial Award. The novel concerns

Doob's martingale inequality (2,106 words) [view diff] exact match in snippet view article find links to article

inequality is a submartingale relative to a filtration of the underlying probability space. The probability measure on the sample space of the martingale will

Jeffreys prior (2,591 words) [view diff] exact match in snippet view article find links to article

\theta } . That is, the relative probability assigned to a volume of a probability space using a Jeffreys prior will be the same regardless of the parameterization

Multiple-try Metropolis (1,265 words) [view diff] exact match in snippet view article find links to article

uses a Gaussian distribution centered on the current point in the probability space, of the form Q ( x ′ ; x t ) = N ( x t ; σ 2 I ) {\displaystyle

Divergence-from-randomness model (2,339 words) [view diff] exact match in snippet view article find links to article

But, more commonly, in order to establish the simpler case when the probability space is invariant in IR, the term independence assumption is often made

Consistent pricing process (289 words) [view diff] exact match in snippet view article find links to article

"prices" of assets in a market. It is a stochastic process in a filtered probability space ( Ω , F , { F t } t = 0 T , P ) {\displaystyle (\Omega ,{\mathcal

Algorithmic Lovász local lemma (2,501 words) [view diff] exact match in snippet view article find links to article

limited dependence. Given a finite set of bad events {A1, ..., An} in a probability space with limited dependence amongst the Ais and with specific bounds on

Novikov's condition (334 words) [view diff] exact match in snippet view article find links to article

(X_{t})_{0\leq t\leq T}} is a real valued adapted process on the probability space ( Ω , ( F t ) , P ) {\displaystyle \left(\Omega ,({\mathcal {F}}_{t})

Girsanov theorem (1,568 words) [view diff] exact match in snippet view article find links to article

W t } {\displaystyle \{W_{t}\}} be a Wiener process on the Wiener probability space { Ω , F , P } {\displaystyle \{\Omega ,{\mathcal {F}},P\}} . Let X

Free convolution (1,138 words) [view diff] exact match in snippet view article find links to article

commutative probability space with law μ {\displaystyle \mu } and Y {\displaystyle Y} is a random variable in the same non commutative probability space with

Conditional probability distribution (2,162 words) [view diff] exact match in snippet view article find links to article

Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} be a probability space, G ⊆ F {\displaystyle {\mathcal {G}}\subseteq {\mathcal {F}}} a σ

Kubilius model (255 words) [view diff] exact match in snippet view article find links to article

Kubilius model relies on a clarification and extension of a finite probability space on which the behaviour of additive arithmetic functions can be modeled

Ergodic theory (3,727 words) [view diff] exact match in snippet view article find links to article

(For a probability space, μ ( X ) = 1. ) {\displaystyle {\bar {f}}={\frac {1}{\mu (X)}}\int f\,d\mu .\quad {\text{ (For a probability space, }}\mu (X)=1

Bhattacharyya angle (210 words) [view diff] exact match in snippet view article find links to article

of distance between two probability measures defined on a finite probability space. It is defined as Δ ( p , q ) = arccos ⁡ BC ⁡ ( p , q ) {\displaystyle

Free independence (688 words) [view diff] exact match in snippet view article find links to article

on. Let ( A , ϕ ) {\displaystyle (A,\phi )} be a non-commutative probability space, i.e. a unital algebra A {\displaystyle A} over C {\displaystyle \mathbb

Feller process (699 words) [view diff] exact match in snippet view article find links to article

needed] Every adapted right continuous Feller process on a filtered probability space ( Ω , F , ( F t ) t ≥ 0 ) {\displaystyle (\Omega ,{\mathcal {F}},({\mathcal

Graph dynamical system (1,387 words) [view diff] exact match in snippet view article find links to article

corresponding probabilities. The matching probability space of update sequences induces a probability space of SDS maps. A natural object to study in

Martingale pricing (618 words) [view diff] exact match in snippet view article find links to article

Suppose the state of the market can be represented by the filtered probability space, ( Ω , ( F t ) t ∈ [ 0 , T ] , P ~ ) {\displaystyle (\Omega ,({\mathcal

Martingale representation theorem (586 words) [view diff] exact match in snippet view article find links to article

{\displaystyle B_{t}} be a Brownian motion on a standard filtered probability space ( Ω , F , F t , P ) {\displaystyle (\Omega ,{\mathcal {F}},{\mathcal

Small-bias sample space (2,439 words) [view diff] exact match in snippet view article find links to article

space, ϵ {\displaystyle \epsilon } -biased generator, or small-bias probability space) is a probability distribution that fools parity functions. In other

Degenerate distribution (616 words) [view diff] exact match in snippet view article find links to article

zero: Let X: Ω → ℝ be a real-valued random variable defined on a probability space (Ω, ℙ). Then X is an almost surely constant random variable if there

Orbit (dynamics) (1,071 words) [view diff] exact match in snippet view article

dynamics, when one has a "nice" group G {\displaystyle G} acting on a probability space X {\displaystyle X} in a measure-preserving way, an orbit G . x ⊂

Optimal stopping (2,547 words) [view diff] exact match in snippet view article find links to article

) t ≥ 0 {\displaystyle G=(G_{t})_{t\geq 0}} defined on a filtered probability space ( Ω , F , ( F t ) t ≥ 0 , P ) {\displaystyle (\Omega ,{\mathcal {F}}

Characterization of probability distributions (1,031 words) [view diff] exact match in snippet view article find links to article

distribution was described by V.M. Zolotarev [ru] in such manner. On the probability space we define the space X = { X } {\displaystyle {\mathcal {X}}=\{X\}}

Lovász local lemma (2,013 words) [view diff] exact match in snippet view article find links to article

{\mathcal {A}}=\{A_{1},\ldots ,A_{n}\}} be a finite set of events in the probability space Ω. For A ∈ A {\displaystyle A\in {\mathcal {A}}} let Γ ( A ) {\displaystyle

Quantum nonlocality (9,394 words) [view diff] exact match in snippet view article find links to article

Q} . Contrary to the classical set of correlations, when viewed in probability space, Q {\displaystyle Q} is not a polytope. On the contrary, it contains

Semimartingale (1,825 words) [view diff] exact match in snippet view article find links to article

semimartingales. A real-valued process X defined on the filtered probability space (Ω,F,(Ft)t ≥ 0,P) is called a semimartingale if it can be decomposed

Robust statistics (6,376 words) [view diff] exact match in snippet view article find links to article

population: ( Ω , A , P ) {\displaystyle (\Omega ,{\mathcal {A}},P)} is a probability space, ( X , Σ ) {\displaystyle ({\mathcal {X}},\Sigma )} is a measurable

Random graph (2,328 words) [view diff] exact match in snippet view article find links to article

random forest. Consider a given random graph model defined on the probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} and let P

Chain rule (probability) (2,359 words) [view diff] exact match in snippet view article

, P ) {\displaystyle (\Omega ,{\mathcal {A}},\mathbb {P} )} be a probability space. Recall that the conditional probability of an A ∈ A {\displaystyle

Noncrossing partition (758 words) [view diff] exact match in snippet view article find links to article

ϕ ) {\displaystyle ({\mathcal {A}},\phi )} be a non-commutative probability space (See free probability for terminology.), a ∈ A {\displaystyle a\in

Nancy Kress (725 words) [view diff] case mismatch in snippet view article find links to article

Oct./Nov. 2008 John W. Campbell Memorial Award Best Novel (2003): Probability Space, (Tor Sep. 2002) Theodore Sturgeon Award Best Short Science Fiction

Erdős–Tetali theorem (1,718 words) [view diff] exact match in snippet view article find links to article

that the above formula is well-defined. A detailed discussion on the probability space associated with this type of construction may be found on Halberstam

Binomial regression (2,055 words) [view diff] exact match in snippet view article find links to article

zero to one; it is sometimes used for this type of data when the probability space is where interpretation occurs or when the analyst lacks sufficient

Field of sets (3,669 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mu } is in fact a probability measure we speak of a probability space and call its underlying measurable space a sample space. The points

Variance swap (2,172 words) [view diff] exact match in snippet view article find links to article

W=(W_{t})_{0\leq t\leq T}} is a Brownian motion under the filtered probability space ( Ω , F , F , Q ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {F}

Monte Carlo methods in finance (4,172 words) [view diff] exact match in snippet view article find links to article

also Monte Carlo method). Thus if we suppose that our risk-neutral probability space is P {\displaystyle \mathbb {P} } and that we have a derivative H

Pettis integral (2,103 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (\Omega ,{\mathcal {F}},\operatorname {P} )} be a probability space, and let V {\displaystyle V} be a topological vector space with a

Odds (4,074 words) [view diff] exact match in snippet view article find links to article

given odds as a ratio of integers, this can be represented by a probability space of a finite number of equally probable outcomes. These definitions

Uniform integrability (2,519 words) [view diff] exact match in snippet view article find links to article

Suppose ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a probability space. A class C {\displaystyle {\mathcal {C}}} of random variables is uniformly

Affiliated operator (800 words) [view diff] exact match in snippet view article find links to article

operator with ATA = A. Of course in the classical case when X is a probability space and M = L∞ (X), we simply recover the *-algebra of measurable functions

G-expectation (856 words) [view diff] exact match in snippet view article find links to article

differential equation (BSDE) originally developed by Shige Peng. Given a probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )}

Calibration (statistics) (1,438 words) [view diff] exact match in snippet view article

Martin (2009). Multivariate calibration of classifier scores into the probability space (PDF) (PhD thesis). University of Dortmund. M.P. Naeini, G. Cooper

Bound state (2,314 words) [view diff] exact match in snippet view article find links to article

space ( X , A , μ ) {\displaystyle (X,{\mathcal {A}},\mu )} be a probability space associated with separable complex Hilbert space H {\displaystyle H}

Henri Lebesgue (2,242 words) [view diff] exact match in snippet view article find links to article

Lebesgue spine Lebesgue's universal covering problem Lebesgue–Rokhlin probability space Lebesgue–Stieltjes integration Lebesgue–Vitali theorem Blaschke–Lebesgue

Volatility swap (1,748 words) [view diff] exact match in snippet view article find links to article

W=(W_{t})_{0\leq t\leq T}} is a Brownian motion under the filtered probability space ( Ω , F , F , Q ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {F}

Dubins–Schwarz theorem (386 words) [view diff] exact match in snippet view article find links to article

\langle M\rangle _{\infty }=\infty } guarantees that the underlying probability space is rich enough so that the Brownian motion exists. If one removes

Σ-Algebra of τ-past (333 words) [view diff] exact match in snippet view article find links to article

theory. Let τ {\displaystyle \tau } be a stopping time on the filtered probability space ( Ω , A , ( F t ) t ∈ T , P ) {\displaystyle (\Omega ,{\mathcal {A}}

Self-financing portfolio (692 words) [view diff] exact match in snippet view article find links to article

arbitrage-free derivative pricing. Assume we are given a discrete filtered probability space ( Ω , F , { F t } t = 0 T , P ) {\displaystyle (\Omega ,{\mathcal

Stationary process (2,612 words) [view diff] exact match in snippet view article find links to article

Hilbert space of all square-integrable random variables on the given probability space). By the positive definiteness of the autocovariance function, it

Wasserstein metric (5,194 words) [view diff] exact match in snippet view article find links to article

further to yield: Theorem (Kantorovich-Rubenstein duality)—When the probability space Ω {\displaystyle \Omega } is a metric space, then for any fixed K

Bierlein's measure extension theorem (337 words) [view diff] exact match in snippet view article find links to article

1977. Let ( X , A , μ ) {\displaystyle (X,{\mathcal {A}},\mu )} be a probability space and S ⊂ P ( X ) {\displaystyle {\mathcal {S}}\subset {\mathcal {P}}(X)}

Markov's inequality (2,521 words) [view diff] exact match in snippet view article find links to article

{\displaystyle [0,a]} . We separate the case in which the measure space is a probability space from the more general case because the probability case is more accessible

Acceptance set (784 words) [view diff] exact match in snippet view article find links to article

acceptable to the regulator. It is related to risk measures. Given a probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )}

Nancy Kress bibliography (1,561 words) [view diff] case mismatch in snippet view article find links to article

Probability Moon (Tor July 2000) Probability Sun (Tor July 2001) Probability Space (Tor Sep. 2002) Greentrees Crossfire (Tor Feb. 2003) Crucible (Tor

Doob martingale (1,320 words) [view diff] exact match in snippet view article find links to article

X n } {\displaystyle \left\{X_{1},X_{2},\dots ,X_{n}\right\}} on probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},{\text{P}})}

Generic property (1,640 words) [view diff] exact match in snippet view article find links to article

This is the definition in the measure theory case specialized to a probability space. In discrete mathematics, one uses the term almost all to mean cofinite

Stochastic game (2,434 words) [view diff] exact match in snippet view article find links to article

n=0,1,\ldots } , be an increasing sequence of σ-algebras in some probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},{\mathbf {P}

Degree-preserving randomization (1,252 words) [view diff] exact match in snippet view article find links to article

degree preserving graphs from the real graph, we can then create a probability space for characteristics, such as reciprocity and average path length,

Latin letters used in mathematics, science, and engineering (4,242 words) [view diff] exact match in snippet view article find links to article

arbitrary functor a field an event space sigma algebra as part of a probability space, often as F {\displaystyle {\mathcal {F}}} f represents: the unit

Associative algebra (4,261 words) [view diff] exact match in snippet view article find links to article

multiplied pointwise. The set of semimartingales defined on the filtered probability space (Ω, F, (Ft)t≥0, P) forms a ring under stochastic integration.[citation

Bayesian game (3,283 words) [view diff] exact match in snippet view article find links to article

be essentially modeled as having incomplete information, and the probability space of the game still follows the law of total probability. Bayesian games

List of probabilistic proofs of non-probabilistic theorems (1,848 words) [view diff] exact match in snippet view article find links to article

measure-preserving action action of a discrete, countable group on a standard probability space. A number of theorems stating existence of graphs (and other discrete

Mixing (mathematics) (4,728 words) [view diff] exact match in snippet view article

{\displaystyle (X_{t})_{-\infty <t<\infty }} be a stochastic process on a probability space ⁠ ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P}

Dynamical system (7,094 words) [view diff] exact match in snippet view article find links to article

(usually the non-negative integers), X is a set, and (X, Σ, μ) is a probability space, meaning that Σ is a sigma-algebra on X and μ is a finite measure

Maximal function (1,467 words) [view diff] exact match in snippet view article find links to article

in Rn. Let ( X , B , m ) {\displaystyle (X,{\mathcal {B}},m)} be a probability space, and T : X → X a measure-preserving endomorphism of X. The maximal

John W. Campbell Memorial Award for Best Science Fiction Novel (1,892 words) [view diff] case mismatch in snippet view article find links to article

Arabesk Earthlight Connie Willis Passage Bantam Books 2003 Nancy Kress* Probability Space Tor Books David Brin Kiln People Tor Books Robert J. Sawyer Hominids

Freehold (novel) (1,108 words) [view diff] case mismatch in snippet view article

behind Thief of Lives but ahead of Engine City, Heirs of Earth and Probability Space. Freehold was nominated for the 2005 Prometheus Award for best libertarian

Prior probability (6,753 words) [view diff] exact match in snippet view article find links to article

can be taken out of the integral, and as this integral is over a probability space it equals one. Hence we can write the asymptotic form of KL as K L

Étienne Halphen (1,173 words) [view diff] exact match in snippet view article find links to article

functions 1955b Subjective probability 1957 Properties of a discrete probability space invariant under permutation of its points An overview of Halphen's

Itô calculus (4,554 words) [view diff] exact match in snippet view article find links to article

continuous-time stochastic processes, it is assumed that an underlying filtered probability space is given ( Ω , F , ( F t ) t ≥ 0 , P ) . {\displaystyle (\Omega ,{\mathcal

Cantor set (6,396 words) [view diff] exact match in snippet view article find links to article

is an image of any probability, making the Cantor set a universal probability space in some ways. In Lebesgue measure theory, the Cantor set is an example

Point process (4,595 words) [view diff] exact match in snippet view article find links to article

[clarification needed] To define general point processes, we start with a probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} , and a measurable

Quantum cognition (3,486 words) [view diff] exact match in snippet view article find links to article

contextual process, hence it cannot be modeled in a single Kolmogorovian probability space, which justifies the employment of quantum probability models in decision

Bessel's correction (3,236 words) [view diff] exact match in snippet view article find links to article

the variance if we had a discrete random variable on the discrete probability space { 1 , … , n } {\displaystyle \{1,\ldots ,n\}} that had value x k {\displaystyle

Stochastic ordering (2,294 words) [view diff] exact match in snippet view article find links to article

variables ( X α ) α {\displaystyle (X_{\alpha })_{\alpha }} on the same probability space, such that the distribution of X α {\displaystyle X_{\alpha }} is

John Kieffer (1,037 words) [view diff] exact match in snippet view article find links to article

Shannon-McMillan theorem for the action of an amenable group on a probability space", Annals of Probability, 3 (6): 1031–1037, doi:10.1214/aop/1176996230

Hyperfinite equivalence relation (1,671 words) [view diff] exact match in snippet view article find links to article

countable Borel equivalence relation E on a standard non-atomic Borel probability space (X, μ {\displaystyle \mu } ) that admits a Borel transversal is a

Automated trading system (2,914 words) [view diff] exact match in snippet view article find links to article

could be used for trend following strategy: "Consider a complete probability space (Ω, F, P). Let S r {\displaystyle S_{r}} denote the stock price at

Rademacher complexity (3,519 words) [view diff] exact match in snippet view article find links to article

the goal of measuring their ability to classify points drawn from a probability space under arbitrary labellings. When the function class is rich enough

Information bottleneck method (3,604 words) [view diff] exact match in snippet view article find links to article

increased from zero, increasing numbers of features, in the category probability space, snap into focus at certain critical thresholds. The following case

Continuous-time Markov chain (4,240 words) [view diff] exact match in snippet view article find links to article

Let ( Ω , A , Pr ) {\displaystyle (\Omega ,{\cal {A}},\Pr )} be a probability space, let S {\displaystyle S} be a countable nonempty set, and let T =

Émery topology (287 words) [view diff] exact match in snippet view article find links to article

(\Omega ,{\mathcal {A}},\{{\mathcal {F_{t}}}\},P)} be a filtered probability space, where the filtration satisfies the usual conditions and T ∈ ( 0

Intensity of counting processes (748 words) [view diff] exact match in snippet view article find links to article

s {\displaystyle \Lambda (t)=\int _{0}^{t}\lambda (s)ds} . Given probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )}

Dempster–Shafer theory (5,098 words) [view diff] exact match in snippet view article find links to article

Events of this kind would not be modeled as distinct entities in probability space as they are here in mass assignment space. Rather the event "Red or

Network science (9,906 words) [view diff] exact match in snippet view article find links to article

graph model or p* is a notational framework used to represent the probability space of a tie occurring in a social network. An alternate approach to network

Dimension doubling theorem (360 words) [view diff] exact match in snippet view article find links to article

Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} be a probability space. For a d {\displaystyle d} -dimensional Brownian motion W ( t ) {\displaystyle

Option on realized variance (1,072 words) [view diff] exact match in snippet view article find links to article

W=(W_{t})_{0\leq t\leq T}} is a Brownian motion under the filtered probability space ( Ω , F , F , Q ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {F}

Itô–Nisio theorem (523 words) [view diff] exact match in snippet view article find links to article

E {\displaystyle E} -valued random variables defined on the same probability space S n = ∑ i = 1 n X n {\displaystyle S_{n}=\sum _{i=1}^{n}X_{n}} μ n

Donsker classes (538 words) [view diff] exact match in snippet view article find links to article

{\mathcal {F}}} be a collection of square integrable functions on a probability space ( X , A , P ) {\displaystyle ({\mathcal {X}},{\mathcal {A}},P)} .

Kramkov's optional decomposition theorem (503 words) [view diff] exact match in snippet view article find links to article

(\Omega ,{\mathcal {A}},\{{\mathcal {F}}_{t}\},P)} be a filtered probability space with the filtration satisfying the usual conditions. A d {\displaystyle

Option on realized volatility (1,091 words) [view diff] exact match in snippet view article find links to article

W=(W_{t})_{0\leq t\leq T}} is a Brownian motion under the filtered probability space ( Ω , F , F , Q ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {F}

Configuration model (4,487 words) [view diff] exact match in snippet view article find links to article

variation is referred to as micro-canonical because it defines a uniform probability space where all possible graphs consistent with the given degree sequence

Conditioning (probability) (6,865 words) [view diff] exact match in snippet view article

where x runs over (−1,1), and these events are a partition of the probability space. In order to avoid paradoxes (such as the Borel's paradox), the following

Freddy Delbaen (668 words) [view diff] exact match in snippet view article find links to article

he introduced the concept of (coherent) risk measure on a finite probability space. Delbaen later generalized the concept to general probability spaces

Deficiency (statistics) (1,347 words) [view diff] exact match in snippet view article

{F}}} . Le Cam defined the statistical model more abstract than a probability space with a family of probability measures. He also didn't use the term

Kernel embedding of distributions (9,770 words) [view diff] exact match in snippet view article find links to article

substantial portion of the probability mass to all regions of the probability space (much of which may not be represented in the training examples). In

German Army cryptographic systems of World War II (4,418 words) [view diff] exact match in snippet view article find links to article

cryptologists seem to have never realised the true reduction of Enigma's probability space under real conditions, particularly those reductions arising from

Ball covariance (2,438 words) [view diff] exact match in snippet view article find links to article

Y)} be a B {\displaystyle B} -valued random variable defined on a probability space such that ( X , Y ) ∼ θ , X ∼ μ {\displaystyle (X,Y)\sim \theta ,X\sim

Flow-based generative model (7,345 words) [view diff] exact match in snippet view article find links to article

distributions after scaling and translation of the input distributions in log-probability space. For p , q ∈ Δ n − 1 {\displaystyle \mathbf {p} ,\mathbf {q} \in \Delta