Semi-discrete, semi-linear SPDEs

Georgiou, Nicos, Joseph, Mathew, Khoshnevisan, Davar and Shiu, Shang-Yuan (2015) Semi-discrete, semi-linear SPDEs. Annals of Applied Probability, 25 (5). pp. 2959-3006. ISSN 1050-5164

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Consider an infinite system
of interacting Ito diffusions, started at a nonnegative deterministic bounded initial profile. We study local and global features of the solution under standard regularity assumptions on the nonlinearity σ. We will show that, locally in time, the solution behaves as a collection of independent diffusions. We prove also that the k-th moment Lyapunov exponent is frequently of sharp quadratic order k^2, in contrast to the continuous-space stochastic heat equation whose k-th moment Lyapunov exponent can be of sharp cubic order. When the underlying walk is transient and the noise level is sufficiently low, we prove also that the solution is a.s. uniformly dissipative provided that the initial profile is regular enough.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Nicos Georgiou
Date Deposited: 26 Jan 2016 13:51
Last Modified: 07 Mar 2017 04:41

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