Decompositions of stochastic convolution driven by a white-fractional Gaussian noise

doi:10.1007/s11464-021-0950-5

Front. Math. China

2021, Vol. 16

Issue (4) : 1063-1073 https://doi.org/10.1007/s11464-021-0950-5

RESEARCH ARTICLE

Decompositions of stochastic convolution driven by a white-fractional Gaussian noise

Ran WANG(

), Shiling ZHANG

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

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Abstract

Let $u = {u (t, x); (t, x) ∈ ℝ + × ℝ}$ be the solution to a linear stochastic heat equation driven by a Gaussian noise, which is a Brownian motion in time and a fractional Brownian motion in space with Hurst parameter $H ∈ (0, 1)$ : For any given $x ∈ ℝ (resp ., t ∈ ℝ +)$ , we show a decomposition of the stochastic process $t → u (t, x) (r e s p ., x → u (t, x))$ as the sum of a fractional Brownian motion with Hurst parameter H/2 (resp., H) and a stochastic process with C^∞-continuous trajectories. Some applications of those decompositions are discussed.

Keywords Stochastic heat equation fractional Brownian motion (fBm) path regularity law of the iterated logarithm

Corresponding Author(s): Ran WANG

Issue Date: 11 October 2021

Cite this article:

Ran WANG,Shiling ZHANG. Decompositions of stochastic convolution driven by a white-fractional Gaussian noise[J]. Front. Math. China, 2021, 16(4): 1063-1073.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0950-5
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I4/1063

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