Structural properties of semilinear SPDEs driven by cylindrical stable processes
Analysis of PDEs
2011-10-06 v2 Probability
Abstract
We consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise.We investigate structural properties of the solutions like Markov, irreducibility, stochastic continuity, Feller and strong Feller properties, and study integrability of trajectories. The obtained results can be applied to semilinear stochastic heat equations with Dirichlet boundary conditions and bounded and Lipschitz nonlinearities.
Cite
@article{arxiv.0810.5063,
title = {Structural properties of semilinear SPDEs driven by cylindrical stable processes},
author = {Enrico Priola and Jerzy Zabczyk},
journal= {arXiv preprint arXiv:0810.5063},
year = {2011}
}
Comments
This version is almost identical with the one published in Probab. Theory Related Fields. We have also corrected some constants appearing in Theorem 4.16 and Hypothesis 5.6