Sample path properties of parabolic SPDEs with non constant coefficients

2024/10/31 by Dalang, Robert C., Sanz-Solé, Marta
#60G15 #60G60 #FOS: Mathematics #Primary 60H15 #Probability (math.PR) #Secondary 60H20

paper · doi:10.48550/arxiv.2410.23995

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.

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