LYAPUNOV EXPONENTS AND SYNCHRONISATION BY NOISE FOR SYSTEMS OF SPDES

• 成果类型: Article
• 署名作者: Gess, Benjamin; Tsatsoulis, Pavlos
• 署名单位: University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1690
• 发表日期: 2024
• 页码: 1903-1953
• 关键词: small random perturbations; DYNAMICAL-SYSTEMS; random attractors; monte-carlo; fluctuations; MODEL; EQUATIONS; time

摘要

Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the invariant measure, with careful control on the resulting error terms. As a consequence of these estimates, synchronisation by noise is deduced for systems of stochastic reaction-diffusion equations for the first time.