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Stochastic differential equations

Physics Reports, 1976
Abstract In chapter I stochastic differential equations are defined and classified, and their occurrence in physics is reviewed. In chapter II it is shown for linear equation show a differential equation for the averaged solution is obtained by expanding in ατ c , where α measures the size of the fluctuations and τ c their autocorrelation time. This
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Stochastic differential equations

2011
In this chapter we present some basic results on stochastic differential equations, hereafter shortened to SDEs, and we examine the connection to the theory of parabolic partial differential equations.
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MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Stochastics and Dynamics, 2008
In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic ...
Boufoussi, B., Mrhardy, N.
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Stochastic Differential Equations

2016
Let \(\mathbf{W} = (W^{1},\ldots,W^{m})\) be an m-dimensional Brownian motion, and let $$\displaystyle{\boldsymbol{\sigma }= (\sigma _{ij})_{1\leq i\leq d,1\leq j\leq m}: [0,\infty ) \times \mathbb{R}^{d} \rightarrow \mathbb{R}^{d} \times \mathbb{R}^{m}}$$ and $$\displaystyle{\boldsymbol{\mu }= (\mu ^{1},\ldots,\mu ^{d}): [0,\infty ) \times \
Paola Lecca   +4 more
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Stochastic partial differential equations

2014
Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2.
Peter K. Friz, Martin Hairer
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Stochastic Differential Equations

2012
This chapter represents the core of the book. Building on the general theory introduced in previous chapters, stochastic differential equations (SDEs) are presented as a key mathematical tool for relating the subject of dynamical systems to Wiener noise.
Vincenzo Capasso, David Bakstein
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Stochastic Differential Equations

2019
Abstract In this chapter we introduce stochastic differential equations (SDEs) and discuss existence and uniqueness questions. The geometric and linear equations are studied in some detail and their most important properties are derived. We then discuss the connection between SDEs and partial differential equations (PDEs).
V. Lakshmikantham, S.G. Deo
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