Quantitative normal approximations for the stochastic fractional heat\n equation

2020/07/29 by Obayda Assaad, Assaad, Obayda, David Nualart +5 · 2 citations
Economics, Econometrics and Finance · Mathematics · #60F05 #60G15 #60H07 #60H15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2007.15148

openalex publication_date 2020/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we present a it quantitative central limit theorem for the\nstochastic fractional heat equation driven by a a general Gaussian\nmultiplicative noise, including the cases of space-time white noise and the\nwhite-colored noise with spatial covariance given by the Riesz kernel or a\nbounded integrable function. We show that the spatial average over a ball of\nradius R converges, as R tends to infinity, after suitable renormalization,\ntowards a Gaussian limit in the total variation distance. We also provide a\nfunctional central limit theorem. As such, we extend recently proved similar\nresults for stochastic heat equation to the case of the fractional Laplacian\nand to the case of general noise.\n

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• Temporal properties of the stochastic fractional heat equation with rough dependence in space
• Growth rates for the Hölder coefficients of the linear stochastic fractional heat equation with rough dependence in space

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