Dynamic Systems and Applications 25 (2016) 153-174 SINGULARLY PERTURBED MULTI-SCALE SWITCHING DIFFUSIONS
نویسندگان
چکیده
This work is concerned with singularly perturbed multi-scale switching diffusions. The switching process is a two-time-scale Markov chain with slow and fast components subject to weak and strong interactions. In the model, there are two small parameters ε and δ. The first one highlights the fast changing part of the switching process, and the other delineates the slow diffusion. We treat the case that ε and δ are related in that ε = δ . Under certain conditions, asymptotic expansions of the probability densities for the underlying processes are developed. The approach is constructive and the asymptotic series are rigorously justified with error bounds. AMS (MOS) Subject Classification. 60J35, 35C20, 35K45
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