Large deviations for stochastic nonlinear systems of slow–fast diffusions with non-Gaussian Lévy noises. (January 2023)

• Record Type: Journal Article
• Authors: Yuan, Shenglan; Schilling, René; Duan, Jinqiao
• Is Part Of: International journal of non-linear mechanics. Volume 148(2023)
• Publication Date: 2023-01
• Subjects: 60F10 -- 49L25 -- 37H10; Large deviations -- Slow–fast dynamical system -- Lévy noises -- Viscosity solutions -- Comparison principle; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2022.104304
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: We establish the large deviation principle for the slow variables in slow–fast dynamical system driven by both Brownian noises and Lévy noises. The fast variables evolve at much faster time scale than the slow variables, but they are fully inter-dependent. We study the asymptotics of the logarithmic functionals of the slow variables in the three regimes based on viscosity solutions to the Cauchy problem for a sequence of partial integro-differential equations. We also verify the comparison principle for the related Cauchy problem to show the existence and uniqueness of the limit for viscosity solutions. Highlights: Establish the large deviation principle for the slow variables in stochastic slow–fast system. Investigate the asymptotics of logarithmic functionals of slow variables in three regimes. Verify the comparison principle for the related Cauchy problem. Show the existence and uniqueness of the limit for viscosity solutions.