A remark on normalizations in a local principle of large deviations

2019/11/10 by Logachov, A. V., Suhov, Y. M., Vvedenskaya, N. D. +1
#60F10 #60J75 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1911.03981

Abstract

This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. We establish rough exponential asymptotic for the probability that a sample path of a normalized process lies in a neighborhood of a given nonnegative continuous function. We propose a variety of normalization schemes for which the large deviation functional preserves its natural integral form.

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