Regularity properties of the solution to a stochastic heat equation driven by a bifractional Brownian motion on S2

Qingbo Wang and Zhenlong Chen

Statistics & Probability Letters, 2025, vol. 226, issue C

Abstract: This paper investigates the linear stochastic heat equation on the unit sphere S2 driven by an infinite dimensional bifractional Brownian noise. We prove the existence and uniqueness of the solution and establish the regularity properties of its sample path. Specifically, we examine the properties of strong local nondeterminism and derive the exact uniform modulus for the solution.

Keywords: Stochastic heat equation; Spherical random fields; Strong local nondeterminism; Uniform modulus of continuity (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110500

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