## Electronic Communications in Probability

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

#### 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.

#### Article information

Source
Electron. Commun. Probab. Volume 16 (2011), paper no. 32, 337-352.

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

https://projecteuclid.org/euclid.ecp/1465261988

Digital Object Identifier
doi:10.1214/ECP.v16-1636

Mathematical Reviews number (MathSciNet)
MR2819657

Zentralblatt MATH identifier
1225.60104

Rights

#### Citation

Fournier, Nicolas; Printems, Jacques. Stability of the stochastic heat equation in $L^1([0,1])$. Electron. Commun. Probab. 16 (2011), paper no. 32, 337--352. doi:10.1214/ECP.v16-1636. https://projecteuclid.org/euclid.ecp/1465261988.

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