Two-Time-Scale Switching Jump Diffusions

Abstract

This chapter is concerned with jump diffusions involving Markovian switching regimes. In the models, there are a finite set of regimes or configurations and a switching process that dictates which regime to take at any given instance. At each time t, once the configuration is determined by the switching process, the dynamics of the system follow a jump-diffusion process. It evolves until the next jump takes place. Then the post-jump location is determined and the process sojourns in the new location following the evolution of another jump-diffusion process and so on. The entire system consists of random switches and jump-diffusive motions.