Sample path properties of parabolic SPDEs with non constant coefficients
Probability
2025-05-27 v1
Abstract
We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and has a spatially homogeneous covariance. We prove existence and uniqueness of a random field solution to this SPDE. Our main result concerns the space-time sample path regularity of its solution.
Keywords
Cite
@article{arxiv.2410.23995,
title = {Sample path properties of parabolic SPDEs with non constant coefficients},
author = {Robert C. Dalang and Marta Sanz-Solé},
journal= {arXiv preprint arXiv:2410.23995},
year = {2025}
}
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28 pages