Key points are not available for this paper at this time.
This work is concerned with diffusion processes having fast and slow components. It was known that under suitable assumptions the slow component can be approximated by the Markov process with averaged characteristics. In this work, asymptotic expansions for the solutions of the Kolmogorov backward equations are constructed and justified. Certain probabilistic conclusions and examples are also provided.
Khas’minskiĭ et al. (2004) studied this question.