Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on ${\mathbb{S}}^2$

Xiaohong Lan; Yimin Xiao

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arXiv · 1807.05867

Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on ${\mathbb{S}}^2$

Xiaohong Lan·Yimin Xiao

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Abstract

We study the stochastic heat equation driven by an additive infinite dimensional fractional Brownian noise on the unit sphere $\mathbb{S}^{2}$. 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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Xiaohong Lan, Yimin Xiao. 2018-07-13. Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on ${\mathbb{S}}^2$. https://arxiv.org/abs/1807.05867

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