On large deviation theorems for Markov processes on a compact domain
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概要
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Large deviation theorems of the Donsker-Varadhan type are studied. Those theorems for a family of stochastic processes converging to a Markov process have already been obtained by the present author. In this paper, these theorems are modified so that they cover the case where each process is killed on exiting a compact domain. The general theory of large deviations of such a type is mentioned at two levels; the state-space level and the path-space level, and applied to the study of the principal eigenvalue of the generator of a Markov process. It is shown that the principal eigenvalue converges as the probability law of the corresponding Markov process converges. As a typical example, the converging family of Markov processes in the homogenization problem is investigated.
- 京都工芸繊維大学の論文
- 2000-02-25
京都工芸繊維大学 | 論文
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