Results 321 to 330 of about 351,513 (382)

Strong approximation of monotone stochastic partial differential equations driven by multiplicative noise

Stochastics and Partial Differential Equations: Analysis and Computations, 2018
We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener process.
Zhihui Liu, Zhonghua Qiao
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Stochastic Partial Differential Equations

2015
A natural generalisation of the finite-dimensional diffusions are stochastic partial differential equations. In this chapter we focus on the Allen-Cahn equation introduced in Section 5.7 in one spatial dimension. Section 5.7 gives the main theorem and a rough outline of its proof.
Anton Bovier, Frank den Hollander
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On stochastic partial differential equations with Unbounded coefficients

Potential Analysis, 1992
Existence, uniqueness and approximations of parabolic Itô equations are considered. The well-weighted Sobolev spaces are used. In particular stochastic partial differential equations (SPDE) with unbounded coefficients, SPDE whose coefficients grow faster than linear functions and SPDE on manifolds are discussed.
Gyöngy, István, Krylov, Nicolai V.
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Strong Averaging Principle for Slow–Fast Stochastic Partial Differential Equations with Locally Monotone Coefficients

Applied Mathematics and Optimization, 2019
This paper is devoted to proving the strong averaging principle for slow–fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally monotone ...
Wei Liu, M. Röckner, Xiaobin Sun, Yingchao Xie   +3 more
semanticscholar   +1 more source

Fully Nonlinear Stochastic Partial Differential Equations

SIAM Journal on Mathematical Analysis, 1996
The authors are concerned with the following stochastic partial differential equation: \[ du(t, .)= L(t, ., u, Du, D^2u) dt+ \langle b(t, .)Du+ h(t, .)u, dW(t) \rangle, \qquad u(0)= u_0, \tag{1} \] where \(L\), \(b\) and \(h\) are suitable functions and \(W\) is an \(\mathbb{R}^N\)-valued Brownian motion.
G. Da Prato, Tubaro, Luciano
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INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Stochastics and Dynamics, 2008
In this paper, we study the existence of an invariant foliation for a class of stochastic partial differential equations with a multiplicative white noise. This invariant foliation is used to trace the long term behavior of all solutions of these equations.
Lu, Kening, Schmalfuß, Björn
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The Numerical Approximation of Stochastic Partial Differential Equations

Milan Journal of Mathematics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jentzen, A., Kloeden, P. E.
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Stochastic Partial Differential Equations

2012
A brief discussion on the relevance of stochastic partial differential equations (SPDEs) in Sect. 9.1 is followed by a review of the type of SPDEs studied in the mathematical literature (Sect. 9.2). Section 9.3 shows that SPDEs can be solved by the methods in Chaps. 7 and 8 via time and space discretization.
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Stochastic Partial Differential Equations

2016
So far, we have discussed discrete interface models. Taking their (mesoscopic) continuum limit, as a time evolution of interfaces or some other related physical order parameters, one would expect to obtain stochastic partial differential equations (SPDEs), which are partial differential equations having stochastic terms such as a space-time Gaussian ...
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Stochastic Partial Differential Equations

2007
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Ito Type Levy Processes and Stochastic Integrals Stochastic Differential Equations of Levy Type Comments Scalar Equations of First Order Introduction Generalized Ito's Formula Linear Stochastic Equations Quasilinear ...
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