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...lization of the [[Cauchy–Schwarz inequality]] to integrals of [[stochastic processes]]. ...inzo Watanabe]] and plays a fundamental role in their extension of Ito's [[stochastic integral]] to square-integrable martingales.<ref>[http://www-math.mit.edu/~ ...

|title = Stochastic Models in Operations Research: Stochastic Processes and Operating Characteristics |chapter = 5.8 Superposition of Renewal Processes ...

...728976| title = On the Stochastic Matrices Associated with Certain Queuing Processes| journal = [[The Annals of Mathematical Statistics]]| volume = 24| issue = ...ete-time Markov chain on a countable state space <math>S</math> having a [[Stochastic matrix|transition probability matrix]] <math>P</math> with elements <math>p ...

...|author=Karatzas, Ioannis|author2=Shreve, Steven|title=Brownian motion and stochastic calculus|publisher=Springer|year=2012|pages=215|isbn=978-0-387-97655-6 |url ...ions|editor=Arató, M.|editor2=Vermes, D.|editor3=Balakrishnan, A. V.|title=Stochastic Differential Systems|series=Lectures Notes in Control and Information Scien ...

{{Short description|Term in stochastic calculus}} ...="block">dX_t=\frac{dY_t}{Y_{t-}},\quad X_0=0.</math>In layperson's terms, stochastic logarithm of <math>Y</math> measures the cumulative percentage change in < ...

...relating the [[expected value|expected]] [[upper bound]] and [[Continuous stochastic process|regularity properties]] of a [[Gaussian process]] to its [[entropy] ...3-319-40519-3_2|title=V. N. Sudakov's work on expected suprema of Gaussian processes|conference=High Dimensional Probability|volume=VII|editor-first1 =Christian ...

In [[stochastic calculus]], the '''Boué–Dupuis formula''' is [[Calculus of variations|varia *The [[infimum]] runs over all [[Stochastic Process|processes]] which are [[progressively measurable]] with respect to the [[filtration ( ...

*{{Citation |last=Cox, Miller |title=The theory of stochastic processes |location=London |publisher=Chapman and Hall Ltd |year=1963}}. [[Category:Eponymous theorems of physics]] ...

...nal |first=Jean |last=Jacod |date=1980 |title=Weak and Strong Solutions of Stochastic Differential Equations |journal=Stochastics |volume=3 |pages=171-191 |doi=1 ...er=24 |pages=1–13 |title=The Yamada–Watanabe theorem for mild solutions to stochastic partial differential equations |volume=18}}<!-- auto-translated from German ...

...''a''.<ref name=Jacobs>{{cite book|last=Jacobs|first=Kurt|title=Stochastic Processes for Physicists|year=2010|publisher=Cambridge University Press|isbn=97811394 Assuming <math> W(0) = 0 </math> , due to the continuity of Wiener processes, each path (one sampled realization) of Wiener process on <math> (0,t) </ma ...

...al''' of a [[semimartingale]] ''X'' is the unique strong solution of the [[stochastic differential equation]] <math display="block">dY_t = Y_{t-}\,dX_t,\quad\qua ...0.1007/BF00534595|s2cid=118181229 |issn=0044-3719|doi-access=free}}</ref> Stochastic exponential plays an important role in the formulation of [[Girsanov theore ...

...are used in the theory of [[point process]]es and related fields such as [[stochastic geometry]] and [[spatial statistics]].<ref name="stoyan1995stochastic"/> ...n1995stochastic">D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. ''Stochastic geometry and its applications'', volume 2. Wiley Chichester, 1995.</ref> ...

{{Short description|Type of stochastic process}} ...stically interacting components. IPS are the continuous-time analogue of [[stochastic cellular automata]]. ...

{{Short description|Mathematical theorem in stochastic processes}} ...adapted process|adapted]] and [[integrable stochastic process|integrable]] stochastic process as the sum of a [[Martingale (probability theory)|martingale]] and ...

*{{citation | author = R. M. Dudley | title = Uniform central limit theorems | publisher = Cambridge University Press | location = Cambridge, UK | year [[Category:Stochastic processes]] ...

In the mathematical theory of [[stochastic processes|random processes]], the '''Markov chain central limit theorem''' has a conclusion somewhat s ...I. and Lifšic, B. A. (1978). "Central limit theorem for stationary Markov processes." ''Soviet Mathematics, Doklady'', '''19''', 392–394. (English translation ...

{{about|random point processes||Campbell's theorem (geometry)}} ...203496930 | title = Statistical Inference and Simulation for Spatial Point Processes | series = C&H/CRC Monographs on Statistics & Applied Probability | volume ...

...technical condition in various [[Central limit theorem|probabilistic limit theorems]]. ...dence condition and applications to moment inequalities|journal=Stochastic Processes and Their Applications|language=en|volume=84|issue=2|pages=313–342|doi=10.1 ...

...f>{{Cite book | last1 = Reiss | first1 = R. D. | title = A Course on Point Processes | doi = 10.1007/978-1-4613-9308-5 | series = Springer Series in Statistics ...K_{ji}</math> where the numbers <math>K_{ji}</math> define a (countable) [[stochastic matrix]] <math>(K_{ji})</math> i.e. ...

[[Category:Stochastic processes]] [[Category:Probability theorems]] ...