Fractional stochastic heat equation with piecewise constant coefficients

2019/10/28 by Yuliya Mishura, Kostiantyn Ralchenko, Mishura, Yuliya +5
Mathematics · #35R60 #60G22 #60H15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:35R60 #msc:60G22 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1910.12655

29 pages

arxiv created 2019/10/28 · arxiv updated 2019/10/29

Abstract

We introduce a fractional stochastic heat equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infinite-dimensional fractional Brownian motion. We characterize the fundamental solution of its deterministic part, and prove the existence and the uniqueness of its solution.

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