Singularly perturbed multidimensional switching diffusions with fast and slow switchings

This work is concerned with singularly perturbed switching diffusions with fast and slow components. The diffusion component of the joint process is m ultidimensional and the diffusive motion evolves an order of magnitude slow er than that of the jumps or the switchings. The jump component may be deco mposed into several groups. There is one group consisting of transient stat es, and all other groups involve recurrent states. Within each group, there are rapid switchings. Among different groups, the switchings occur relativ ely infrequently. Under simple conditions, an asymptotic expansion of the p robability density is developed; error bounds and justification of the expa nsion are provided. (C) 1999 Academic Press.