Solutions of stochastic partial differential equations considered as Dirichlet processes
Laurent, Denis
Bernoulli, Tome 10 (2004) no. 2, p. 783-827 / Harvested from Project Euclid
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We consider the parabolic stochastic partial differential equation $$u(t,x)=\Phi(x)+\int_0^t Lu(s,x)+f(s,x,u(s,x),Du(s,x))\,\d s$$ $$+\int_0^t g_i(s,x,u(s,x),Du(s,x))\,\d B^i_s,$$/ \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.
Publié le : 2004-10-14
Classification:  comparison theorem,  Dirichlet processes,  stochastic partial differential equation 
@article{1099579156,
     author = {Laurent, Denis},
     title = {Solutions of stochastic partial differential equations considered as Dirichlet processes},
     journal = {Bernoulli},
     volume = {10},
     number = {2},
     year = {2004},
     pages = { 783-827},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1099579156}
}

Laurent, Denis. Solutions of stochastic partial differential equations considered as Dirichlet processes. Bernoulli, Tome 10 (2004) no. 2, pp.  783-827. http://gdmltest.u-ga.fr/item/1099579156/