ISSN:
1000-9574
Keywords:
Key words Singularly perturbed Markov chain, Occupation measure, Aggregation, Absorbing state, Weak convergence, Switching diffusion
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1991MR Subject Classification 60J27, 60B10, 34E05, 60F17
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states. It focuses on both unscaled and scaled occupation measures. Under mild conditions, a mean-square estimate is obtained. By averaging the fast components, we obtain an aggregated process. Although the aggregated process itself may be non-Markovian, its weak limit is a Markov chain with much smaller state space. Moreover, a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s101140050013
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