Stability of the stochastic heat equation in $L^1([0,1])$

Nicolas Fournier (Université Paris Est)
Jacques Printems (Université Paris Est)

Abstract


We consider the white-noise driven stochastic heat equation on $[0,1]$ with Lipschitz-continuous drift and diffusion coefficients. We derive an inequality for the $L^1([0,1])$-norm of the difference between two solutions. Using some martingale arguments, we show that this inequality provides some estimates which allow us to study the stability of the solution with respect the initial condition, the uniqueness of the possible invariant distribution and the asymptotic confluence of solutions.

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Pages: 337-352

Publication Date: May 30, 2011

DOI: 10.1214/ECP.v16-1636

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