2013/10/15 by Xiaopeng Chen, Chen, Xiaopeng, A. J. Roberts +4
Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37L55 #Quantum chaos and dynamical systems #Secondary 37D10 #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.DS #msc:37D10 #msc:37L55
paper · pdf · doi:10.48550/arxiv.1310.4062
33pages. arXiv admin note: substantial text overlap with arXiv:1210.5924
arxiv created 2013/10/15 · openalex publication_date 2013/10/15 · arxiv updated 2013/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stochastic center manifolds theory are crucial in modelling the dynamical behavior of complex systems under stochastic influences. A multiplicative ergodic theorem on Hilbert space is proved to be satisfied to the exponential trichotomy condition. Then the existence of stochastic center manifolds for infinite dimensional random dynamical systems is shown under the assumption of exponential trichotomy. The theory provides a support for the discretisations of nonlinear stochastic partial differential equations with space-time white noise.