Precise high moment asymptotics for parabolic Anderson model with\n log-correlated Gaussian field

2019/09/03 by Yang-Yang Lyu, Lyu, Yangyang
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1909.01031

openalex publication_date 2019/09/03 · openalex created_date 2022/07/19 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the continuous parabolic Anderson model (PAM)\ndriven by a time-independent log-correlated Gaussian field (LGF). We obtain an\nasymptotic result of\n
mathbbE
exp
Bigg

frac12
sum
limits_\nj,k=1^N
int₀^t
int₀^t
gamma(B_j(s)-B_k(r))drds
Bigg

qquad(N
rightarrow\n
infty) which is composed of the independent Brownian motions B_j(s) \nand the function \γ approximating to a logarithmic potential at 0, such\nas the covariances of massive free field and Bessel field. Based on the\nasymptotic result, we get the precise high moment asymptotics for Feynman-Kac\nformula of the PAM with LGF.\n

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