Singularly Perturbed Switching Diffusions: Rapid Switchings and Fast Diffusions

A. M. Il'in, R. Z. Khasminskii and G. Yin
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A. M. Il'in: Ural Branch of the Russian Academy of Sciences
R. Z. Khasminskii: Wayne State University
G. Yin: Wayne State University

Journal of Optimization Theory and Applications, 1999, vol. 102, issue 3, No 5, 555-591

Abstract: Abstract Motivated by many problems in optimization and control, this paper is concerned with singularly perturbed systems involving both diffusions and pure jump processes. Two models are treated. In the first model, the jump process changes very rapidly by comparison with the diffusion processes. In the second model, the diffusions change rapidly in comparison with the jump process. Asymptotic expansions are developed for the transition density vectors via a constructive method; justification of the asymptotic expansions and analysis of the remainders are provided.

Keywords: Kolmogorov forward equation; singular perturbation; asymptotic expansion (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1022698023010

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