Homogenization of nonlinear stochastic partial differential equations in a general ergodic environment
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Date
Authors
Razafimandimby, Paul Andre
Woukeng, Jean Louis
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor & Francis
Abstract
In this article, we show that the concept of sigma-convergence associated to
stochastic processes can tackle the homogenization of stochastic partial differential
equations. In this regard, the homogenization of a stochastic nonlinear partial
differential equation is addressed. Using some deep compactness results such as
the Prokhorov and Skorokhod theorems, we prove that the sequence of solutions of
this problem converges in probability towards the solution of an equation of the
same type. To proceed with, we use the concept of sigma-convergence for stochastic
processes, which takes into account both the deterministic and random behaviours
of the solutions of the problem.
Description
Keywords
Algebras with mean value, Stochastic homogenization, Stochastic partial differential equations, Wiener process
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Citation
Paul André Razafimandimby & Jean Louis Woukeng (2013) Homogenization of Nonlinear Stochastic Partial Differential Equations in a General Ergodic Environment, Stochastic Analysis and Applications, 31:5, 755-784, DOI: 10.1080/07362994.2013.817237