Large deviation principles for fully coupled multiscale multivalued stochastic systems

2025/12/11 by Huijie Qiao, Qiao, Huijie
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #Stochastic processes and financial applications #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2512.10311

Abstract

This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a general stochastic differential equation. First, we establish the large deviation principle for the slow component at any fixed time by leveraging viscosity solutions of second-order Hamilton-Jacobi-Bellman equations involving multivalued operators. Subsequently, we illustrate the theoretical results through a concrete example.

Citations

• Large deviations of multiscale multivalued McKean-Vlasov stochastic systems
• Asymptotic behaviors of multiscale multivalued stochastic systems with small noises
• Large Deviations for Small Noise Diffusions Over Long Time
• Central Limit Type Theorem and Large Deviation Principle for Multi-Scale McKean-Vlasov SDEs
• Distribution-Dependent SDEs for Landau Type Equations
• Distribution dependent SDEs for Landau type equations
• On large deviations of coupled diffusions with time scale separation
• Large Deviations Principle by viscosity solutions: the case of\n diffusions with oblique Lipschitz reflections

Related

• Large deviation for multivalued stochastic differential equations
• Large deviations of multiscale multivalued McKean-Vlasov stochastic systems
• A large deviation principle for Markovian slow-fast systems
• Large Deviation Principle for Some Measure-Valued Processes
• Large deviation principle for stochastic integrals and stochastic\n differential equations driven by infinite-dimensional semimartingales