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Existence of almost periodic solutions of stochastic differential equations with periodic coefficients

  • Mohamed-Ahmed Boudref EMAIL logo und Ahmed Berboucha
Veröffentlicht/Copyright: 1. März 2017
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Abstract

In this work, under some conditions, we will prove that a scalar stochastic differential equation with periodic coefficients admits almost periodic solutions.

MSC 2010: 60H10; 34C27; 34G10

Dedicated to to Professor Hamid Osmanov



Communicated by Vyacheslav L. Girko


References

[1] Amério L. and Prousse G., Almost Periodic Functions and Functional Equations, Van Nostrand, New York, 1971. 10.1007/978-1-4757-1254-4Suche in Google Scholar

[2] Arnold L. and Tudor C., Stationary and almost periodic solutions of almost periodic affine stochastic differential equations, Stochastics Stochastics Rep. 64 (1998), no. 3–4, 177–193. 10.1080/17442509808834163Suche in Google Scholar

[3] Bezandry P. H. and Diagana T., Existence of almost periodic solutions to some stochastic differential equations, Appl. Anal. 86 (2007), no. 7, 819–827. 10.1080/00036810701397788Suche in Google Scholar

[4] Bezandry P. H. and Diagana T., Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations, Electron. J. Differential Equations 2009 (2009), no. 111, 1–14. 10.1155/2009/575939Suche in Google Scholar

[5] Blot J., Une approche variationnelle des orbites quasi-périodiques des systèmes Hamiltoniens, Ann. Sci. Math. Qué. 13 (1989), no. 2, 7–32. Suche in Google Scholar

[6] Da Prato G., Periodic and almost periodic solutions for semilinear stochastic equations, Stoch. Anal. Appl. 13 (1995), no. 1, 13–33. 10.1080/07362999508809380Suche in Google Scholar

[7] Dorogovtsev A. Y., The existence of periodic solutions of an abstract stochastic equation. Asymptotic periodicity of solutions of the Cauchy problem (in Russian), Teor. Veroyatn. Mat. Stat. Kiev 39 (1988), 47–52; translation in Theory Probab. Math. Statist. 39 (1989), 55–60. Suche in Google Scholar

[8] Doss H., Liens entre équations différentielles stochastiques et ordinaires, C. R. Acad. Sci. Paris Ser. A 283 (1976), 939–942. Suche in Google Scholar

[9] Doss H., Sur l’existence, l’unicité et le comportement asymptotique des solutions d’équations différentielles stochastiques, Ann. Inst. Henri Poincaré, Nouv. Sér. Sect. B 14 (1978), no. 2, 198–214. Suche in Google Scholar

[10] Doss H. and Postelnicu G., Sur une approche probabiliste d’un problème d’analyse semi-classique, J. Funct. Anal. 224 (2005), 352–370. 10.1016/j.jfa.2004.07.019Suche in Google Scholar

[11] Guikhman I. and Skorokhod A., Introduction à la théorie des processus aléatoires, Mir, Moscow, 1980. Suche in Google Scholar

[12] Guillotin-Plantard N., Introduction au calcul stochastique, Technical Report, Polycopié Université de Lyon 1, France, 2009. Suche in Google Scholar

[13] Has’minskii R. Z., Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, USA, 1980. 10.1007/978-94-009-9121-7Suche in Google Scholar

[14] Karatzas I. and Shreve S., Brownian Motion and Stochastic Calculus, Springer, New York, 1988. 10.1007/978-1-4684-0302-2Suche in Google Scholar

[15] Massera J. L., The existence of periodic solutions of systems of differential equations, Duke Math. J. 17 (1950), 457–475. 10.1215/S0012-7094-50-01741-8Suche in Google Scholar

[16] Mellah O. and De Fitte P. R., Countre examples to mean square almost periodicity of the solutions of some SDES with almost periodic coefficients, preprint 2012, https://arxiv.org/abs/1208.6384. Suche in Google Scholar

[17] Morozan T., Periodic solutions of stochastic discrete-time systems, Roumaine Math. Appl. 32 (1987), 351–363. Suche in Google Scholar

[18] Morozan T. and Tudor C., Almost periodic solutions of affine Itô equations, Stoch. Anal. Appl. 7 (1989), no. 4, 451–474. 10.1080/07362998908809194Suche in Google Scholar

[19] Tudor C., Almost periodic solutions of affine stochastic evolution equations, Stochastics Stochastics Rep. 38 (1992), no. 4, 251–266. 10.1080/17442509208833758Suche in Google Scholar

[20] Vârsan C., Asymptotic almost periodic solutions for stochastic differential equations, Tohoku Math. J. (2) 41 (1986), 609–618. 10.1007/BFb0002677Suche in Google Scholar

[21] Yoshizawa T., Stability Theory by Ljapounov’s Second Method, Publ. Math. Soc. Japan. 9, Mathematical Society of Japan, Tokyo, 1966. Suche in Google Scholar

Received: 2016-12-13
Accepted: 2017-1-25
Published Online: 2017-3-1
Published in Print: 2017-3-1

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