2021/12/11 by Nhu N. Nguyen, Nguyen, Nhu N., George Yin +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #60F05 #60F10 #60J60 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2112.06081
openalex publication_date 2021/12/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and stochastic acceleration in a random environment. Our effort is to carry out asymptotic analysis to establish large deviations principles. Our focus is on obtaining the desired results for systems under weaker conditions. When the fast-varying process is a diffusion, neither Lipschitz continuity nor linear growth needs to be assumed. Our approach is based on combinations of the intuition from Smoluchowski-Kramers approximation, and the methods initiated in [34] relying on the concepts of relatively large deviations compactness and the identification of rate functions. When the fast-varying process is under a general setup with no specified structure, the paper establishes the large deviations principle of the underlying system under the assumption on the local large deviations principles of the corresponding first-order system.