Probabilistic analysis of a class of impulsive linear random differential equations via density functions

An important class of non-homogeneous first-order linear random differential equations subject to an infinite sequence of square impulses with random intensity is studied. In applications, these equations are useful to model the dynamics of a population with periodic harvesting and migration under uncertainties. The solution is explicitly obtained via the first probability density function assuming an arbitrary joint density for all model parameters. Probabilistic stability analysis is carried out through the densities of the random sequences of minima and maxima. All the theoretical results are fully illustrated through two numerical examples. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study examines a class of non-homogeneous first-order linear random differential equations subject to an infinite sequence of random intensity square impulses. These equations are useful in modeling the dynamics of a population with periodic harvesting and migration under uncertainties. The solution is explicitly obtained via the first probability density function, and probabilistic stability analysis is conducted through the densities of random sequences of minima and maxima.