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

   
@article{ECP1636,
	author = {Nicolas Fournier and Jacques Printems},
	title = {Stability of the stochastic heat equation in $L^1([0,1])$},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {},
	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.},
	pages = {no. 32, 337-352},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1636},    
        url = {http://ecp.ejpecp.org/article/view/1636}}