An alternative expression of Di Paola and Falson's formula for stochastic dynamics

TL;DR

This paper presents a more general and numerically efficient alternative expression to Di Paola and Falson's formula for stochastic dynamics under Poisson noise, linking it to Marcus integrals.

Contribution

It introduces a new, more versatile expression for the formula that improves numerical performance and broadens applicability in stochastic dynamics analysis.

Findings

The alternative expression is applicable under more general conditions.

It shows significantly improved numerical implementation.

It is a special case of Marcus integrals.

Abstract

Di Paola and Falsone's formula is widely used in studying stochastic dynamics of nonlinear systems under Poisson white noise. In this short communication, an alternative expression is presented. Compared to Di Paola and Falsone's original expression, the alternative one is applicable under more general condition, and shows significantly improved performance in numerical implementation. The alternative expression turns out to be a special case of the Marcus integrals.