# A random string with reflection in a convex domain

Abstract : We study the motion of a random string in a convex domain $O$ in $\R^d$, namely the solution of a vector-valued stochastic heat equation, confined in the closure of $O$ and reflected at the boundary of $O$. We study the structure of the reflection measure by computing its Revuz measure in terms of an infinite-dimensional integration by parts formula. Our method exploits recent results on weak convergence of Markov processes with log-concave invariant measures.
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Document type :
Preprints, Working Papers, ...
2010
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https://hal.archives-ouvertes.fr/hal-00473274
Contributor : Said Bounebache <>
Submitted on : Wednesday, April 14, 2010 - 9:25:29 PM
Last modification on : Wednesday, October 12, 2016 - 1:03:56 AM

### Identifiers

• HAL Id : hal-00473274, version 1
• ARXIV : 1004.1197

### Citation

Said Bounebache. A random string with reflection in a convex domain. 2010. 〈hal-00473274〉

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