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  2. Standard probability space - Wikipedia

    en.wikipedia.org/wiki/Standard_probability_space

    A measurable subset of a standard probability space is a standard probability space. It is assumed that the set is not a null set, and is endowed with the conditional measure. See (Rokhlin 1952, Sect. 2.3 (p. 14)) and (Haezendonck 1973, Proposition 5). Every probability measure on a standard Borel space turns it into a standard probability space.

  3. Probability space - Wikipedia

    en.wikipedia.org/wiki/Probability_space

    In probability theory, a probability space or a probability triple (,,) is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements: [1] [2]

  4. Space–bandwidth product - Wikipedia

    en.wikipedia.org/wiki/Space–bandwidth_product

    In holography, the space–bandwidth product determines the resolution and quality of the reconstructed holographic image. The SBP sets a limit on the amount of information that can be recorded and reconstructed. In digital holography, the SBP of a holographic imaging system can be calculated by analyzing at the recorded interference pattern. [3]

  5. Filtration (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Filtration_(probability...

    Let (,,) be a probability space and let be an index set with a total order (often , +, or a subset of +).. For every let be a sub-σ-algebra of .Then := is called a filtration, if for all .

  6. Gaussian probability space - Wikipedia

    en.wikipedia.org/wiki/Gaussian_probability_space

    In probability theory particularly in the Malliavin calculus, a Gaussian probability space is a probability space together with a Hilbert space of mean zero, real-valued Gaussian random variables. Important examples include the classical or abstract Wiener space with some suitable collection of Gaussian random variables.

  7. Sample-continuous process - Wikipedia

    en.wikipedia.org/wiki/Sample-continuous_process

    Let (Ω, Σ, P) be a probability space.Let X : I × Ω → S be a stochastic process, where the index set I and state space S are both topological spaces.Then the process X is called sample-continuous (or almost surely continuous, or simply continuous) if the map X(ω) : I → S is continuous as a function of topological spaces for P-almost all ω in Ω.

  8. Skorokhod's representation theorem - Wikipedia

    en.wikipedia.org/wiki/Skorokhod's_representation...

    In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of a pointwise convergent sequence of random variables defined on a common probability space.

  9. Probabilistic metric space - Wikipedia

    en.wikipedia.org/wiki/Probabilistic_metric_space

    A probability metric D between two random variables X and Y may be defined, for example, as (,) = | | (,) where F(x, y) denotes the joint probability density function of the random variables X and Y.