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Semi-discrete, semi-linear SPDEs
journal contribution
posted on 2023-06-12, 06:37 authored by Nicos GeorgiouNicos Georgiou, Mathew Joseph, Davar Khoshnevisan, Shang-Yuan ShiuConsider 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 s. 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.
History
Publication status
- Published
File Version
- Published version
Journal
Annals of Applied ProbabilityISSN
1050-5164Publisher
The Institute of Mathematical StatisticsExternal DOI
Issue
5Volume
25Page range
2959-3006Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes