Asymptotic Expansions of Solutions of Integro-Differential Equations for Transition Densities of Singularly Perturbed Switching Diffusions: Rapid Switchings

摘要

This work develops asymptotic expansions for solutions of integro-differential equations arising from transition densities of singularly perturbed switching-diffusion processes. The underlying processes have two components, namely the switching component and the diffusion component. Processes with rapid switchings are examined here. Under suitable conditions, it is proved that the asymptotic expansion is uniformly valid in the domain of interest.