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Singularly Perturbed Switching Diffusions: Rapid Switchings and Fast Diffusions

Author

Listed:
  • A. M. Il'in

    (Ural Branch of the Russian Academy of Sciences)

  • R. Z. Khasminskii

    (Wayne State University)

  • G. Yin

    (Wayne State University)

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.

Suggested Citation

  • A. M. Il'in & R. Z. Khasminskii & G. Yin, 1999. "Singularly Perturbed Switching Diffusions: Rapid Switchings and Fast Diffusions," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 555-591, September.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:3:d:10.1023_a:1022698023010
    DOI: 10.1023/A:1022698023010
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    Cited by:

    1. Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489, arXiv.org, revised Sep 2010.
    2. G. Yin, 2001. "On Limit Results for a Class of Singularly Perturbed Switching Diffusions," Journal of Theoretical Probability, Springer, vol. 14(3), pages 673-697, July.

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