Large deviations in a population dynamics with catastrophes

TL;DR

This paper establishes a large deviation principle for a class of Markov processes modeling population dynamics with catastrophes, revealing how rare large fluctuations occur in such systems.

Contribution

It proves the large deviation principle for population processes with linear growth and uniform catastrophes, providing insights into the trajectories of rare events.

Findings

Large deviation principle is established for the process.

Optimal trajectories of large fluctuations are characterized.

The model describes population dynamics with uniform catastrophes.

Abstract

The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear growth and uniform catastrophes, where an eliminating portion of the population is chosen uniformly. The large deviation result provides an optimal trajectory of large fluctuation: it shows how the large fluctuations occur for this class of processes.