This group gathers theorems about stochastic processes, random quantities that evolve in time, including martingales, Brownian motion and random walks. It covers stopping and convergence results for martingales, the calculus of random processes and the change of measure, the construction of processes from consistent families of distributions, and the link between random processes and differential equations. A theorem belongs here when its cited article places it in the theory of stochastic processes.
All Stochastic Processes and Martingales
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Donsker's Theorem (Wikipedia)
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is known as a random walk. Define the diffusively rescaled random walk (partial-sum process) by W ( n ) ( t ) := S ⌊
Optional Stopping Theorem (Wikipedia)
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that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected
Kolmogorov Extension Theorem (Wikipedia)
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of finite-dimensional distributions will define a stochastic process. It is credited to the English mathematician
Itô's lemma (Wikipedia)
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to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart
Girsanov theorem, Wikipedia
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or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure. The theorem
Wiener-Khinchin theorem (Wikipedia)
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In applied mathematics and statistics, the Wiener-Khinchin theorem or Wiener-Khintchine theorem
Skorokhod's embedding theorem (Wikipedia)
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collection of random variables as a Wiener process (Brownian motion) evaluated at a collection of stopping
Feynman-Kac formula, Wikipedia
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link between parabolic partial differential equations and stochastic processes. In 1947, when Kac and Feynman were both faculty
Doob decomposition theorem - Wikipedia
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In the theory of stochastic processes in discrete time, a part of the mathematical
Chung-Fuchs theorem, Wikipedia
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Fuchs, states that for a particle undergoing a zero-mean random walk in m-dimensions, it is certain to come back infinitely
Structure theorem for Gaussian measures - Wikipedia
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theorem for Gaussian measures shows that the abstract Wiener space construction is essentially the only way
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