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2016 | 3 | 1 | 85-103

Tytuł artykułu

Almost automorphic solution for some stochastic evolution equation driven by Lévy noise with coefficients S2−almost automorphic

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
In this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson S2−almost automorphic) processes in distribution. We establish some interesting results on the functional space of such processes like an composition theorems. Next, under some suitable assumptions, we establish the existence, the uniqueness and the stability of the square-mean almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Lévy noise in case when the functions forcing are both continuous and S2−almost automorphic. We provide an example to illustrate ours results.

Wydawca

Rocznik

Tom

3

Numer

1

Strony

85-103

Opis fizyczny

Daty

otrzymano
2016-03-11
zaakceptowano
2016-06-13
online
2016-07-07

Twórcy

  • Université Gaston Berger de Saint-Louis, UFR SAT, Département de Mathématiques, B.P. 234, Saint-Louis Sénégal

Bibliografia

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  • [15] M. A. Diop, K. Ezzinbi and M. M. Mbaye, Measure theory and square-mean pseudo almost periodic and automorphic process: Application to stochastic evolution equations, Bulletin of the Malaysian Mathematical Sciences Society, DOI: 10.1007/s40840-015-0278-y. [Crossref]
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  • [24] J. Liang, G.M. N’Guérékata, T-J. Xiao and J. Zhang, Some properties of pseudo-almost automorphic functions and applications to abstract differential equations, Nonlinear Analysis, Theory, Methods and Applications 70, (7), (2009), 2731–2735.
  • [25] J. Liang, J. Zhang and T-J. Xiao, Composition of pseudo almost automorphic and asymptotically almost automorphic functions, Journal of Mathematical Analysis and Applications 340, (2), (2008), 1493–1499.
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  • [30] S. Peszat, J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise, Cambridge University Press, (2007).
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  • [35] T-J. Xiao, J. Liang and J. Zhang, Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces, Semigroup Forum, 76, (3), (2008), 518–524. [WoS][Crossref]
  • [36] T-J. Xiao, X-X. Zhu and J. Liang, Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications, Nonlinear Analysis, Theory, Methods and Applications, 70, (11), (2009), 4079–4085.
  • [37] S. Zaidman, Almost automorphic solutions of some abstract evolutions equations, Istituto Lombardo. Accademia di Scienze e Lettere, Estrato dai Rendiconti, Classe di Scienze (A), 110, (1976), 578–588.

Typ dokumentu

Bibliografia

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