PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
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
  • [1] D. Applebaum, Lévy Process and Stochastic Calculus, second edition, Cambridge University Press, (2009).
  • [2] J. Blot, G.M.Mophou, G.M. N’Guérékata and D. Pennequin, Weighted pseudo almost automorphic functions and applications to abstract differential equations, Nonlinear Analysis, Theory, Methods and Applications, 71, (3–4), (2009), 903–909.
  • [3] P. Bezandry and T. Diagana, Existence of almost periodic solutions to some stochastic differential equations, Appl. Anal, 86, (2007), 819–827. [Crossref]
  • [4] P. Bezandry, Existence of almost periodic solutions to some functional integro-differential stochastic evolution equations, Statist. Probab. Lett. 78, (2008), 2844–2849. [WoS]
  • [5] P. H. Bezandry and T. Diagana, Square-mean almost periodic solutions nonautonomous stochastic differential equations, Electron. J. Differential Equations, 2007, No. 117, 10 pp.
  • [6] P. Bezandry and T. Diagana, Existence of S2-almost periodic solutions to a class of nonautonomous stochastic evolution equations, Electron. J. Qual. Theory Differ. Equ. 35, (2008), 1–19.
  • [7] S.Bochner, Uniform convergence of monotone sequences of functions, Proc. Natl. Acad. Sci. USA, 47, (1961), 582-585. [Crossref]
  • [8] P. Cieutat, S. Fatajou and G.M. N’Guérékata, Composition of pseudo almost periodic and pseudo almost automorphic functions and applications to evolution equations, Applicable Analysis 89, (1), (2010), 11–27. [WoS][Crossref]
  • [9] Y.K. Changa, Z. H. Zhaoa, G.M. N’Guérékata and R. Mab, Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations, Nonlinear Analysis: Real World Applications 12, (2011), 1130–1139.
  • [10] Z. Chen andW. Lin Square-mean pseudo almost automorphic process and its application to stochastic evolution equations, Journal of Functional Analysis, 261, (2011), 69–89.
  • [11] T. Diagana and M. M.Mbaye, Existence results for some nonlinear hyperbolic partial differential equations, Electron. J. Differ. Equ., Vol. 2015 (2015), No. 241, 1-10.
  • [12] T. Diagana and M. M. Mbaye, Square-mean almost periodic solutions to some singular stochastic differential equations, Applied Mathematics Letters, 54, (2016), 48–53. [Crossref]
  • [13] M. A. Diop, K. Ezzinbi and M. M. Mbaye, Measure theory and S2− pseudo almost periodic and automorphic process: Application to stochastic evolution equations, Afrika Matematika, 26, (5), (2015), 779-812.
  • [14] M. A. Diop, K. Ezzinbi and M. M. Mbaye, Existence and global attractiveness of a pseudo almost periodic solution in the p-th mean sense for stochastic evolution equation driven by a fractional Brownian, Stochastics: An International Journal Of Probability And Stochastic Processes, 87, (6), (2015), 1061-1093.
  • [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]
  • [16] K. Ezzinbi and G.M. N’Guérékata, Almost automorphic solutions for some partial functional differential equations, Journal of Mathematical Analysis and Applications 328, (1), (2007), 344–358.
  • [17] K. Ezzinbi and G.M. N’Guérékata, Almost automorphic solutions for partial functional differential equations with infinite delay, Semigroup Forum 75, (1), (2007), 95–115. [Crossref][WoS]
  • [18] K. Ezzinbi, V. Nelson and G.M. N’Guérékata, C(n)-almost automorphic solutions of some nonautonomous differential equations, Cubo 10, (2), (2008), 61–74.
  • [19] M. M. Fu, Almost automorphic solutions for nonautonomous stochastic differential equations, Journal ofMathematical Analysis and Applications. 393, (2012), 231–238.
  • [20] M.M. Fu and Z.X. Liu, Square-mean almost automorphic solutions for some stochastic differential equations, Proc. Amer. Math. Soc. 133, (2010), 3689-3701. [WoS]
  • [21] J.A. Goldstein and G.M. N’Guérékata, Almost automorphic solutions of semilinear evolution equations, Proc. Amer. Math. Soc. 133, (2005), 2401-2408. [WoS]
  • [22] M. Kamenskii, O. Mellah, P. Raynaud de Fitte, Weak averaging of semilinear stochastic differential equations with almost periodic coefficients, J. Math. Anal. Appl. 427 (2015) 336–364
  • [23] O. Mellah, P. Raynaud de Fitte, Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients, Electron. J. Differential Equations 2013 (91) (2013) 1–7.
  • [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.
  • [26] Z. Liu and K. Sun, Almost automorphic solutions for stochastic differential equations driven by Lévy noise, J. Funct. Anal., 266, (3), (2014), 1115–1149. [WoS]
  • [27] G.M. N’Guérékata, Almost automorphic solutions to second-order semilinear evolution equations, Nonlinear Analysis, Theory, Methods and Applications 71, (12), (2009), e432–e435.
  • [28] G.M. N’Guérékata, Topics in almost Automorphy, Springer-verlag, New York, 2005.
  • [29] G.M. N’Guérékata and A. Pankov, Stepanov-like almost automorphic functions and monotone evolution equations, Nonlinear Anal. TMA 68, (2008), 2658–2667.
  • [30] S. Peszat, J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise, Cambridge University Press, (2007).
  • [31] G. Da Prato and C. Tudor, Periodic and almost periodic solutions for semilinear stochastic evolution equations, Stoch. Anal. Appl. 13, (1995), 13–33. [Crossref]
  • [32] G.D. Prato and J. Zabczyk, Stochastics Equations in Infinite Dimensions, Encyclopedia of Mathematics and its Applications 44, Cambridge University Press, Cambridge, (1992).
  • [33] C. Tudor, Almost periodic solutions of affine stochastic evolutions equations, Stoch. Stoch. Rep, 38, (1992), 251–266. [Crossref]
  • [34] Y. Wang, Z.X. Liu, Almost periodic solutions for stochastic differential equations with Lévy noise, Nonlinearity, 25, (2012), 2803–2821. [Crossref]
  • [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
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_msds-2016-0005
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.