Asymptotics of the solutions of the stochastic lattice wave equation
Ryzhik, Lenya; Olla, Stefano; Komorowski, Tomasz (2013), Asymptotics of the solutions of the stochastic lattice wave equation, Archive for Rational Mechanics and Analysis, 209, 2, p. 455-494. http://dx.doi.org/10.1007/s00205-013-0626-8
TypeArticle accepté pour publication ou publié
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)We consider the long time limit for the solutions of a discrete wave equation with weak stochastic forcing. The multiplicative noise conserves energy, and in the unpinned case also conserves momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds for both square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic.
Subjects / KeywordsOrnstein-Uhlenbeck equation; Stochastic processes; Wave equation
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Komorowski, Tomasz; Olla, Stefano; Ryzhik, Lenya; Spohn, Herbert (2020) Article accepté pour publication ou publié