Abstract
This work presents asymptotic results for singularly perturbed switching diffusions consisting of diffusion components and a pure jump component. The states of the pure jump component are divisible into a number of groups having recurrent states. An aggregated process is obtained by collecting all the states in each recurrent group as one state. We show the aggregated process converges weakly to a switching diffusion with generator being an average with respect to the quasi-stationary distribution of the jump process.
This research was supported in part by the National Science Foundation under grant DMS-9529738, and in part by Wayne State University.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35359-3_40
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Yin, G., Kniazeva, M. (1999). Time-Scale Separation and State Aggregation in Singularly Perturbed Switching Diffusions. In: Chen, S., Li, X., Yong, J., Zhou, X.Y. (eds) Control of Distributed Parameter and Stochastic Systems. IFIP Advances in Information and Communication Technology, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35359-3_36
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DOI: https://doi.org/10.1007/978-0-387-35359-3_36
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