Periodic Solutions for Stochastic Differential Equations Driven by General Counting Processes: Application to Malaria | Zendy

KOUAME Yao Simplice | Zendy; Modeste N’zi | Zendy

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Periodic 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.

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