Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise

2016/07/14 by Xia Chen, Chen, Xia, Yaozhong Hu +5
Economics, Econometrics and Finance · Mathematics · #60G15 #60H07 #60H10 #65C30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1607.04092

openalex publication_date 2016/07/14 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance structure of a fractional Brownian motion with Hurst parameter greater than 1/4 and less than 1/2 in the space variable.

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