A class of Langevin equations with Markov switching involving strong damping and fast switching

Abstract

This work is devoted to a class of Langevin equations involving strong damping and fast Markov switching. Modeling using continuous dynamics and discrete events together with their interactions much enlarged the applicability of Langevin equations in a random environment. Strong damping and fast switching are characterized by the use of multiple small parameters, resulting in singularly perturbed systems. The motivation of our work stems from the reduction of complexity for complex systems. Under suitable conditions, it is established that the solutions of the Langevin equations satisfy a large deviations principle. Then, we apply our results to statistical physics problems of a small particle in time-inhomogeneous environment and low temperature. Some connections to other fields in physics are also given.