Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on \mathbbS²

2018/07/13 by Xiaohong Lan, Lan, Xiaohong, Yimin Xiao +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1807.05867

openalex publication_date 2018/07/13 · openalex created_date 2018/08/03 · openalex updated_date 2026/07/28

Abstract

We study the stochastic heat equation driven by an additive infinite dimensional fractional Brownian noise on the unit sphere \mathbbS². The existence and uniqueness of its solution in certain Sobolev space is investigated and sample path regularity properties are established. In particular, the exact uniform modulus of continuity of the solution in time/spatial variable is derived.

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