Article ID Journal Published Year Pages File Type
1153152 Statistics & Probability Letters 2010 7 Pages PDF
Abstract

We compare the large deviations between jump Markov processes and their diffusion approximations for the problem of escape from a domain. It is known that the escape times are generally asymptotically different, leading to a quantitative error. In this paper we show that the escape point can also be different, which implies a qualitative error. In dimension one, for a general class of birth-and-death processes, we show that there always exists a domain [a,b][a,b] such that the jump process asymptotically escapes from aa and its approximation from bb.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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