Degenerate parabolic stochastic partial differential equations
TLDR
In this article, the authors considered the problem of continuous dependence on initial data in the case of degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients, and provided a new and fairly elementary proof of Skorkhod's classical theorem on existence of weak solutions.About:
This article is published in Stochastic Processes and their Applications.The article was published on 2013-12-01 and is currently open access. It has received 120 citations till now. The article focuses on the topics: Stochastic partial differential equation & Hyperbolic partial differential equation.read more
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Stochastic Differential Equations
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
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Stochastic flows and stochastic differential equations
TL;DR: In this article, the authors consider continuous semimartingales with spatial parameter and stochastic integrals, and the convergence of these processes and their convergence in stochastically flows.
References
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Semigroups of Linear Operators and Applications to Partial Differential Equations
TL;DR: In this article, the authors considered the generation and representation of a generator of C0-Semigroups of Bounded Linear Operators and derived the following properties: 1.1 Generation and Representation.
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Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.