An Extension of Massera’s Theorem for N-Dimensional Stochastic Differential Equations

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Titre:	An Extension of Massera’s Theorem for N-Dimensional Stochastic Differential Equations
Auteur(s):	Boudref, Mohamed Ahmed Berboucha, Ahmed Osmanov, Hamid Ibrahim Ouglu
Mots-clés:	stochastic differential equations, periodic solution, Markov process, Massera theorem 1.
Date de publication:	18-déc-2017
Editeur:	IntechOpen
Résumé:	In this chapter, we consider a periodic SDE in the dimension n 2, and we study the existence of periodic solutions for this type of equations using the Massera principle. On the other hand, we prove an analogous result of the Massera’s theorem for the SDE considered.
Description:	The theory of stochastic differential equations is given for the first time by Itô [7] in 1942. This theory is based on the concept of stochastic integrals, a new notion of integral generalizing the Lebesgue–Stieltjes one. The stochastic differential equations (SDE) are applied for the first time in the problems of Kolmogorov of determining of Markov processes [8]. This type of equations was, from the first work of Itô, the subject of several investigations; the most recent include the generalization of known results for EDO, such as the existence of periodic and almost periodic solutions. It has, among others, the work of Bezandry and Diagana [1, 2], Dorogovtsev [4], Vârsan [12], Da Prato [3], and Morozan and his collaborators [10, 11].
URI/URL:	http://dspace.univ-bouira.dz:8080/jspui/handle/123456789/10596
Collection(s) :	Articles

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An Extension of Massera Theorem for NDimensionalStochastic Differential Equations(1).pdf	In this chapter, we consider a periodic SDE in the dimension n 2, and we study the existence of periodic solutions for this type of equations using the Massera principle. On the other hand, we prove an analogous result of the Massera’s theorem for the SDE considered.	239,57 kB	Adobe PDF	Voir/Ouvrir