Decompositions of stochastic convolution driven by a white-fractional Gaussian noise期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Ran WANG Shiling ZHANG

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

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

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