Stopping Time and Control for a Type of Impulsive Stochastic Differential Equation

TL;DR

This paper develops solutions for impulsive stochastic differential equations with control at pulse-times, providing conditions for the randomness and finiteness of expected values, with applications in biological systems like fisheries.

Contribution

It introduces a method to construct solutions for impulsive stochastic differential equations with controlled pulse-times and establishes conditions for their expected values to be finite.

Findings

Solutions constructed under specific control conditions

Sufficient criteria for finite expected values of solutions

Application demonstrated in fishery management

Abstract

The main objective of this paper is the construction of the solution of an impulsive stochastic differential equation, subject to control conditions in the pulse-times and give sufficient conditions for them to be random variables with finite expectation. Such equations are useful in modeling diverse phenomena as biological control and pressure regulating mechanisms. The article ends with an application in fishery.