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...he [[martingale (probability theory)|martingale]]. A [[stochastic process|stochastic series]] ''X'' is an MDS if its [[expected value|expectation]] with respect ...ce than [[independence (probability theory)|independence]], yet most limit theorems that hold for an independent sequence will also hold for an MDS. ...

...k |last=Leon-Garcia |first=Albert |year=1994 |title=Probability and Random Processes for Electrical Engineering |edition=2nd |location=Boston |publisher=Addison ...first=Ward |year=2002 |title=Stochastic-Process Limits, An Introduction to Stochastic-Process Limits and their Application to Queues |location=New York |publishe ...

The '''Doob–Meyer decomposition theorem''' is a theorem in [[stochastic calculus]] stating the conditions under which a [[Martingale (probability t *{{Cite book| last=Doob | first=J. L. | year=1953 | title=Stochastic Processes | publisher=Wiley }} ...

Similar theorems also exist for [[Martingale (probability theory)|martingales]] on filtratio * [[Backward stochastic differential equation]] ...

...ime a particle has spent at a given level. Local time appears in various [[stochastic integration]] formulas, such as [[Tanaka's formula]], if the integrand is n ...math>, the local time of <math>B</math> at the point <math>x</math> is the stochastic process which is informally defined by ...

...ics]], [[mathematics]], [[science]] and [[philosophy]] to draw conclusions about the likelihood of potential events and the underlying mechanics of complex (Related topics: [[set theory]], [[simple theorems in the algebra of sets]]) ...

{{Short description|Stochastic process in probability theory}} In [[probability theory]], an '''empirical process''' is a [[stochastic process]] that characterizes the deviation of the [[empirical distribution ...

|fields = [[Mathematics]], [[Stochastic differential equation]], [[Markovian process]]es ...is well-known for his comprehensive treatise on the theory of [[stochastic processes]] which he co-authored with [[Iosif Gikhman|Gikhman]].<ref name="GikhmanSko ...

...mann theorem''' or '''formula''') is a [[theorem]] of [[Stochastic process|stochastic analysis]]. It expresses the value of some [[function (mathematics)|functio The interpretation of stochastic integrals as divergences leads to concepts such as the [[Skorokhod integral ...

{{Short description|Theorem on changes in stochastic processes}} ...v's theorem''' or the '''Cameron-Martin-Girsanov theorem''' explains how [[stochastic process]]es change under changes in [[measure (probability)|measure]]. The ...

...astic process]]es concerned with geometric and incidence questions. See [[stochastic geometry]]. ...[Hadwiger's theorem]] in the Euclidean setting. Subsequently Hadwiger-type theorems were established in various settings, notably in hermitian geometry, using ...

...scription|Consistent set of finite-dimensional distributions will define a stochastic process}} {{About|a theorem on stochastic processes|a theorem on extension of pre-measure|Hahn–Kolmogorov theorem}} ...

....Л. Чебышев (list of winners of the Chebyshev medal)|url=http://www.ras.ru/about/awards/awdlist.aspx?awdid=10}}</ref> *Nonlinear theory of stationary [[stochastic processes]] ...

The '''fundamental theorems of asset pricing''' (also: '''of arbitrage''', '''of finance'''), in both [ In continuous time, a version of the fundamental theorems of asset pricing reads:<ref>{{Cite book |last=Björk |first=Tomas |title=Arb ...

...ergodic theorem]]. Then he used these theorems to give rigorous proofs of theorems proven by [[R.A. Fisher|Fisher]] and Hotelling related to Fisher's [[maximu ...so he wrote the book ''Stochastic Processes''.<ref>Doob J.L., ''Stochastic Processes''</ref> It was published in 1953 and soon became one of the most influentia ...

***[[Gödel's incompleteness theorems]] **[[Stochastic process]]es ...

{{Short description|Theorem of stationary processes}} ...be written as the sum of two time series, one ''deterministic'' and one ''stochastic''. ...

...be studied in a dual formulation, as a [[coalescing random walk]], or as a stochastic process. We may consider the mutant population on a graph as a random walk Closely related stochastic processes include the [[voter model]], which was introduced by Clifford and Sudbury ( ...

{{Short description|Spectral decomposition theorem of stationary processes' autocorrelations}} ...A. I. Khintchine (1894–1959) on stationary random processes (or stochastic processes) [...] in contexts in which it is not important to distinguish the two appr ...

...]] with mean 0 and variance 1. Let <math>S_n:=\sum_{i=1}^n X_i</math>. The stochastic process <math>S:=(S_n)_{n\in\N}</math> is known as a [[random walk]]. Defin ...Cite journal|title = An invariance principle for certain probability limit theorems|last = Donsker|first = M.D.|journal = Memoirs of the American Mathematical ...