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On Limit Results for a Class of Singularly Perturbed Switching Diffusions

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  • G. Yin

    (Wayne State University)

Abstract

This work is devoted to the weak convergence analysis of a class of aggregated processes resulting from singularly perturbed switching diffusions with fast and slow motions. The processes consist of diffusion components and pure jump components. The states of the pure jump component are naturally divisible into a number of classes. Aggregate the states in each weakly irreducible class by a single state leading to an aggregated process. Under suitable conditions, it is shown that the aggregated process converges weakly to a switching diffusion process whose generator is an average with respect to the quasi-stationary distribution of the jump process.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:3:d:10.1023_a:1017541022565
    DOI: 10.1023/A:1017541022565
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    References listed on IDEAS

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    1. Zhang, Q. & Yin, G., 1997. "Structural properties of Markov chains with weak and strong interactions," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 181-197, October.
    2. 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.
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