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...l Sznitman| doi = 10.1002/cpa.3160370408 | title = Stochastic differential equations with reflecting boundary conditions | journal = Communications on Pure and ...pages = 3–23}}</ref><ref>{{cite journal | title = Stochastic differential equations with reflecting boundary condition in convex regions | first = Hiroshi | la ...

{{Short description|Stochastsic differential equations with terminal condition}} ...g|first2=Jiongmin|date=2007|title=Forward-Backward Stochastic Differential Equations and their Applications|series=Lecture Notes in Mathematics |volume=1702 |ur ...

...xistence and uniqueness of solutions of stochastic functional differential equations|journal=Random Oper. Stoch. Equ.|first1=Max |last1=von Renesse|first2=Micha {{DEFAULTSORT:Stochastic Gronwall inequality}} ...

...cod |date=1980 |title=Weak and Strong Solutions of Stochastic Differential Equations |journal=Stochastics |volume=3 |pages=171-191 |doi=10.1080/1744250800883314 ...ada–Watanabe theorem for mild solutions to stochastic partial differential equations |volume=18}}<!-- auto-translated from German by Module:CS1 translator --></ ...

...|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 ...=Arató, M.|editor2=Vermes, D.|editor3=Balakrishnan, A. V.|title=Stochastic Differential Systems|series=Lectures Notes in Control and Information Sciences |year=198 ...

...e-hui |last4=Huang |first4=Nan-jing |date=2015 |title=On a System of Fuzzy Differential Inclusions |url=https://www.jstor.org/stable/24898205 |journal=Filomat |vol == Second order differential == ...

...journal|first=Boris S.|last=Tsirel'son |title= An Example of a Stochastic Differential Equation Having No Strong Solution|journal= Theory of Probability & Its App [[Category:Stochastic differential equations]] ...

...[[semimartingale]] ''X'' is the unique strong solution of the [[stochastic differential equation]] <math display="block">dY_t = Y_{t-}\,dX_t,\quad\quad Y_0=1,</mat ...0.1007/BF00534595|s2cid=118181229 |issn=0044-3719|doi-access=free}}</ref> Stochastic exponential plays an important role in the formulation of [[Girsanov theore ...

{{short description|Framework for studying stochastic partial differential equations}} ...g a large class of subcritical parabolic [[stochastic partial differential equations]] arising from [[quantum field theory]].<ref>{{cite journal|last1=Hairer|fi ...

...|first1=A. |title=A first course in the numerical analysis of differential equations |date=2009 |publisher=Cambridge Texts in Applied Mathematics, Cambridge Uni ...=S. |title=On the Itô-Alekseev-Gröbner formula for stochastic differential equations |year=2018 |class=math.PR |eprint=1812.09857}}</ref> is a generalization of ...

{{Short description|Stochastic diffusion process in probability theory}} ...nal |title=A Class of Markov Processes Associated with Nonlinear Parabolic Equations |first=H. P. |last=McKean |author-link=Henry McKean |journal=[[Proceedings ...

...r_motion], A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion.</ref> *{{annotated link|Navier&ndash;Stokes equations}} ...

...l form, the ambit field, <math>Y</math>, is defined by a constant plus a [[stochastic integral]], where the [[integral|integration]] is done with respect to a '' The use and development of ambit fields is motivated by the need of flexible stochastic models to describe [[turbulence]]<ref name="turb">Barndorff-Nielsen, O. E., ...

...al kind of [[Parabolic partial differential equation|parabolic]] [[partial differential equation]]s (PDEs) with a quadratic nonlinearity into a [[Heat equation|lin ...irst=Lawrence C. | authorlink=Lawrence C. Evans|title=Partial Differential Equations |publisher=American Mathematical Society |year=2010 |isbn= |edition=2nd |se ...

...ither be translated into a model such as [[Markov chains]] or differential equations, or be treated using tools that directly work on the rule-set in place of a ...s consisting of [[ordinary differential equation]]s without generating the equations directly. For example below is an example rule in the BioNetGen format: ...

...[[joint probability distribution]]s of different sets of coordinates on a stochastic process. The equation was derived independently by both the British mathe ...an indexed collection of [[Random variable|random variables]], that is, a stochastic process. Let ...

{{Short description|Type of stochastic process in probability}} ...|chapter=On Existence and Uniqueness of Reflected Solutions of Stochastic Equations Driven by Symmetric Stable Processes|author=Engelbert, H.J., Kurenok, V.P. ...

...2000 |title=The Hartman–Grobman theorem for Caratheodory-type differential equations in Banach spaces |journal=Nonlinear Analysis |volume=40 |issue=1–8 |pages=9 ...Ludwig Arnold and Peter Imkeller, Normal forms for stochastic differential equations, ''Probab. Theory Relat. Fields'', '''110''':559&ndash;588, 1998.</ref> ...

...1=Benedict |last2=Matthews |first2=Charles |title=Rational Construction of Stochastic Numerical Methods for Molecular Sampling |journal=Applied Mathematics Resea ...ction]] and <math> W(t) </math> is a [[Wiener process]]. This [[stochastic differential equation]] has solutions (denoted <math>X(t) \in \mathbb{R}^N </math> at ti ...

{{Short description|Equations characterizing continuous-time Markov processes}} {{for-multi|the equations in population dynamics|Kolmogorov equations in population dynamics}} ...