Open AccessPeriodic Solutions for Stochastic Differential Equations Driven by General Counting Processes: Application to Malaria
Author(s) -
Kouame Yao Simplice,
Modeste N’zi
Publication year - 2021
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v13n4p1
Subject(s) - uniqueness , mathematics , stochastic differential equation , class (philosophy) , poisson distribution , differential equation , ordinary differential equation , markov chain , mathematical analysis , markov process , statistics , computer science , artificial intelligence
In this paper, a class of periodic stochastic differential equations driven by general counting processes (SDEsGp) is studied. First, an existence-uniqueness result for the solution of general SDEsGp based on Poisson processes with т-periodic stochastic intensity of time t has been given, for some т> 0. Then, using the properties of periodic Markov processes, sufficient conditions for the existence and uniqueness of a periodic solution of the considered equations are obtained. We will then apply the obtained results to the propagation of malaria in a periodic environment.