Diffusion approximation of birth-death processes: Comparison in terms of large deviations and exit points

Khashayar Pakdaman, Michèle Thieullen and Gilles Wainrib

Statistics & Probability Letters, 2010, vol. 80, issue 13-14, 1121-1127

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] such that the jump process asymptotically escapes from a and its approximation from b.

Keywords: Diffusion; approximation; Large; deviations; Exit; points; Jump; process; Birth; and; death (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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