Abstract
We consider the parabolic stochastic partial differential equation \noindent where f and g are supposed to be Lipschitzian and L is a self-adjoint operator associated with a Dirichlet form defined on a finite- or infinite-dimensional space. We prove that it admits a unique solution which is a Dirichlet process and, thanks to Itô's formula for Dirichlet processes, we prove a comparison theorem.
Citation
Denis Laurent. "Solutions of stochastic partial differential equations considered as Dirichlet processes." Bernoulli 10 (5) 783 - 827, October 2004. https://doi.org/10.3150/bj/1099579156
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