Large deviation of long time average for a stochastic process : an alternative method

TL;DR

This paper introduces a straightforward method for calculating the large deviation rate function of long time averages in stochastic jump processes by reducing the problem to solving a PDE for the probability generating function.

Contribution

It proposes an alternative approach that simplifies the computation of large deviation rate functions for stochastic jump processes using PDEs.

Findings

The method effectively computes rate functions for various stochastic jump processes.

The approach simplifies the calculation by linking it to PDE solutions.

It provides a practical tool for analyzing long-term behavior of stochastic systems.

Abstract

We present here a simple method for computing the large deviation of long time average for stochastic jump processes. We show that the computation of the rate function can be reduced to that of a partial differential equation governing the evolution of the probability generating function. The long time limit of this equation, which in many cases can be easily obtained, leads naturally to the rate function.