arXiv subjects

Y. M. Suhov

Publications and source records attributed to Y. M. Suhov.

3 recordsLinked to original sources

arXiv2023

A large deviations principle for birth-death processes with a linear rate of downward jumps

Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically linearly with the population size, while the rate of a jump up (birth) is growing sub-linearly. We establish a large deviation principle under various forms of scaling of the underlying process and the corresponding normalization of the logarithm of the large deviation probabilities. The results show interesting features of dependence of the large deviation functional upon the parameters of the process and the forms of scaling and normalization.

math.PR↗

arXiv2019

A remark on normalizations in a local principle of large deviations

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.

math.PR↗

arXiv2018

A local large deviation principle for inhomogeneous birth-death processes

The paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotics for the probability of excursions of a re-scaled process contained within a neighborhood of a given continuous non-negative function.

math.PR↗