Large Deviation Principle for Multi-Scale Fully Local Monotone Stochastic Dynamical Systems with Multiplicative Noise

2024/02/28 by Wei Hong, Wei Liu, Hong, Wei +3
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2402.18108

openalex publication_date 2024/02/28 · openalex created_date 2024/03/05 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to proving the small noise asymptotic behaviour, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main techniques are based on a combination of the weak convergence approach, the time discretization technique and the theory of pseudo-monotone operator. The main results derived in this paper have broad applicability to various multi-scale models, where the slow component could be such as stochastic porous medium equations, stochastic Cahn-Hilliard equations and stochastic 2D Liquid crystal equations.

Related

• Large deviation principle for a class of stochastic partial differential equations with fully local monotone coefficients perturbed by Lévy noise
• Small time asymptotics for a class of stochastic partial differential equations with fully monotone coefficients forced by multiplicative Gaussian noise
• Large deviations for locally monotone stochastic partial differential equations driven by Levy noise
• Freidlin-Wentzell Type Large Deviation Principle for Multi-Scale Locally Monotone SPDEs
• Large deviations for locally monotone stochastic partial differential equations driven by Lévy noise