Asymptotic behaviours of multiscale multivalued stochastic systems with small noises
Abstract
In this paper, we consider asymptotic behaviours of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with small noises in the slow components, we prove an averaging principle in the strong convergence sense. Moreover, a convergence rate is given in a special case. Next, for these systems, we establish the large deviation principle by the weak convergence approach. Then, for a special case, the rate function is explicitly characterized. Finally, we explain our results with an example.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Differential Equations Analysis
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Proceedings of the Royal Society of Edinburgh Section A Mathematics
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–57
- Publication date
- 16 January 2026
- Language
- EN