Asymptotic expansions of solutions for parabolic systems associated with transient switching diffusions

Abstract

This work develops asymptotic properties for a parabolic system with two-time scales associated with a transient switching diffusion. Although the problem is motivated by stochastic systems, the techniques that we are using are purely analytic. Asymptotic expansions are constructed; their validity is justified.

Keywords:

• singular perturbation
• diffusion
• backward operator
• asymptotic expansion

AMS Subject Classifications:

• 35B25
• 35C20
• 60J60

Acknowledgments

This research was supported in part by the National Science Foundation under DMS-1207667.