Switching Jump Diffusions: Time-Scale Separations
摘要
This chapter is concerned with two-time scale jump diffusions modulated by a continuous-time Markov chain to reduce complexity through an appropriate averaged system. The first part treats switching jump diffusion with fast switching. It demonstrates that the original complex problem can be “replaced” by a limit problem in which the system coeffcients are averaged out with respect to the stationary measures of the switching process. The second part deals with switching jump diffusion models with periodic fast-varying diffusion, and establishes the weak convergence of the process and with explicitly characterization of the limit system. This chapter also discusses numerical solutions for switching jump diffusions.