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2011 Stability of the stochastic heat equation in $L^1([0,1])$
Nicolas Fournier, Jacques Printems
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Electron. Commun. Probab. 16: 337-352 (2011). DOI: 10.1214/ECP.v16-1636

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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Nicolas Fournier. Jacques Printems. "Stability of the stochastic heat equation in $L^1([0,1])$." Electron. Commun. Probab. 16 337 - 352, 2011. https://doi.org/10.1214/ECP.v16-1636

Information

Accepted: 30 May 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1225.60104
MathSciNet: MR2819657
Digital Object Identifier: 10.1214/ECP.v16-1636

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