Logo image
Back
Temporal asymptotics for fractional parabolic Anderson model
Journal article   Open access   Peer reviewed

Temporal asymptotics for fractional parabolic Anderson model

Xia Chen, Yaozhong Hu, Jian Song and Xiaoming Song
Electronic journal of probability, v 23(none)
01 Jan 2018
DOI: https://doi.org/10.1214/18-EJP139
url
https://doi.org/10.1214/18-ejp139View
Published, Version of Record (VoR)CC BY V4.0,  Open
url
https://doi.org/10.1214/18-EJP139View
Published, Version of Record (VoR) Open

Abstract

Mathematics Physical Sciences Science & Technology Statistics & Probability
In this paper, we consider fractional parabolic equation of the form partial derivative u/partial derivative t = (-Delta) (alpha/2) u + u(W) over dot (t, x), where -(-Delta) (alpha/2) with alpha is an element of (0; 2] is a fractional Laplacian and (W) over dot is a Gaussian noise colored both in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result for space-time Hamiltonians driven by ff -stable process. As a byproduct, we obtain the critical values for theta and eta such that E exp (theta(integral(1)(0) integral(1)(0) vertical bar r - s vertical bar(-beta 0) gamma(X-r - X-s)drds)(eta)) is finite, where X is d -dimensional symmetric alpha-stable process and gamma(x) is vertical bar x vertical bar(-beta) or Pi(d)(j=1) vertical bar x(j)vertical bar(-beta j).

Metrics

14 Record Views
14 citations in Web of Science
13 citations in Scopus

Details

InCites Highlights

Data related to this publication, from InCites Benchmarking & Analytics tool:

Collaboration types
Domestic collaboration
International collaboration
Web of Science research areas
Statistics & Probability
Logo image