Some properties of the solution to fractional heat equation with a fractional Brownian noise
Year: 2017
Type: article
Abstract: In this paper, we consider the stochastic heat equation of the form $$\frac{\partial u}{\partial t}=\Delta_{\alpha}u+\frac{\partial ^{2}B}{\partial t\,\partial x}, $$ where $\frac{\partial^{2}B}{\partial t\,\partial x}$ is a fractional Brownian sheet with Hurst indices $H_{1},H_{2}\in(\frac{1}{2},1)$ and $\Delta _{\alpha}=-(-\Delta)^{\alpha/2}$ is a fractional Laplacian operator with $1<\alpha\leq2$ . In particular, when $H_{2}=\frac{1}{2}$ we show that the temporal process $\{u(t,\cdot),0\leq t\leq T\}$ admits a nontrivial p-variation with $p=\frac{2\alpha}{2\alpha H_{1}-1}$ and study its local nondeterminism and existence of the local time.
Source: Advances in Difference Equations
Authors: Dengfeng Xia, Litan Yan
Institutions: Donghua University, Anhui Polytechnic University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,790
OpenAlex ID: W2604873393