Abstract
Consider the stochastic heat equation ∂tu = Lu + Ẇ, where L is the generator of a [Borel right] Markov process in duality. We show that the solution is locally mutually absolutely continuous with respect to a smooth perturbation of the Gaussian process that is associated, via Dynkin's isomorphism theorem, to the local times of the replica-symmetric process that corresponds to L. In the case that L is the generator of a Lévy process on Rd, our result gives a probabilistic explanation of the recent findings of Foondun et al. (Trans Am Math Soc, 2007).
Original language | English |
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Pages (from-to) | 243-260 |
Number of pages | 18 |
Journal | Potential Analysis |
Volume | 34 |
Issue number | 3 |
Early online date | 3 Aug 2010 |
DOIs | |
Publication status | Published - 30 Apr 2011 |
Externally published | Yes |
Keywords
- Dynkin's isomorphism theorem
- local times
- stochastic heat equation