Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2018, Vol. 47(2): 259-276
Lèvy 过程驱动的随机泛函积分—微分方程的概周期解
On Almost Periodic Solutions forStochastic Functional Integro-differential Evolution Equations with Lèvy Noise

XU Liping1,2, LUO Jiaowan1, LI Zhi2,*

1.广州大学数学与信息学院, 广州, 广东, 510006;
2. 长江大学信息与数学学院, 荆州, 湖北, 434023
1. School of Mathematics and Information Sciences,Guangzhou University, Guangzhou, Guangdong, 510006, P. R. China;
2. School of Information and Mathematics,Yangtze University, Jingzhou, Hebei, 434023, P. R. China

收稿日期: 2016-05-27
出版日期: 2018-05-16
2018, Vol. 47(2): 259-276
DOI: 10.11845/sxjz.2016070b

[273 KB]

    /   /   推荐

摘要 本文研究一类Levy过程驱动的无穷维随机泛函积分---微分发展方程.在一些合适的条件下, 使用算子半群理论和不动点方法,这些方程的概周期温和解的存在唯一性被讨论.进一步,为了说明我们的结果,一个例子被提出.
关键词 概周期性随机泛函积分—微分发展方程vy噪声    
Abstract:In this paper, we investigate a class of stochastic functional integro-differential evolution equations with infinite dimensional Lèvy noise. Under some suitable assumptions, the existence and uniqueness of almost periodic mild solutions in distribution to these equations are discussed by means of semigroups of operators and fixed point method. Moreover, an example is given to illustrate our results.
Key wordsAlmost periodicity in distribution    Stochastic functional integro-differential evolution equations       vy noise
PACS:  O211.63  
[1] Abbas, S. and Bahuguna, D., Almost periodic solutions of neutral functional differential equations, Comput. Math. Appl., 2008, 55: 2593-2601.
[2]Arnold, L. and Tudor, C., Stationary and almost periodic solutions of almost periodic affine stochastic differential equations, Stoch. Stoch. Rep., 1988, 64: 177-193.
[3] Bezandry, P., Existence of almost periodic solutions to some functional integro-differential stochastic evolution equations, Stat. Probab. Lett., 2008, 78: 2844-2849.
[4] Bezandry, P. and Diagana, T., Existence of almost periodic solutions to some stochastic differential equations, Appl. Anal., 2007, 86: 819-827.
[5] Bezandry, P. and Diagana, T., Square-mean almost periodic solutions nonautonomous stochastic differential equations, Electron. J. Differ. Equ., 2007, 2007: 1-10.
[6] Bezandry, P. and Diagana, T., Almost Periodic Stochastic Processes, New York: Springer-Verlag, 2011.
[7] Cont, R. and Tankov, P., Financial Modelling with Jump Processes, Financ. Math. Ser., Boca Raton: Chapman & Hall/CRC, 2004.
[8] Da Prato, G. and Tudor, C., Periodic and almost periodic solutions for semilinear stochastic equations, Stoch. Anal. Appl., 1995, 13: 13-33.
[9] Da Prato, G. and Zabczyk, J., Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl., Vol. 44. Cambridge: Cambridge Univ. Press, 1992.
[10] Halanay, A., Periodic and almost periodic solutions to affine stochastic systems, In: Proceedings of the Eleventh International Conference on Nonlinear Oscillations, Budapest, Jànos Bolyai Math. Soc., 1987, 94-101.
[11] Hale, J.K. and Kato, J., Phase space for retarded equations with infinite delay, Funkcialaj Ekvacioj., 1978, 21: 11-41.
[12] Hernàndez, E. and Henriquez, H.R., Existence of periodic solutions of partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl., 1998, 221: 499-522.
[13] Li, Y. and Liu, B., Existence of solution of nonlinear neutral stochastic diferential inclusions with infinite delay, Stoch. Anal. Appl., 2007, 25(2): 397-415.
[14]Li, Z., Liu, K. and Luo, J.W., On almost periodic mild solutions for neutral stochastic evolution equations with infinite delay, Nonlinear Anal., 2014, 110: 182-190.
[15] Liu, Z. and Sun, K., Almost automorphic solutions for stochastic differential equations driven by Lèvy noise, J. Funct. Anal., 2014, 266: 1115-1149.
[16] Luo, J.W. and Taniguchi, T., The existence and uniqueness for non-Lipschitz stochastic neutral delay evolution equations driven by Poisson jumps, Stoch. Dyn., 2009, 9: 135-152.
[17] Kamenskii, M., Mellah, O. and Raynaud de Fitte, P., Weak averaging of semilinear stochastic differential equations with almost periodic coefficients, J. Math. Anal. Appl., 2015, 427: 336-364.
[18] Kannan, D. and Bharucha-Reid, D., On a Stochastic integro-differential evolution of Volterra type, J. Integral Equations, 1985, 10: 351-379.
[19] Pazy, A., Semigroup of Linear Operators and Applications to Partial Differential Equations, New York: Springer-Verlag, 1992.
[20] Peszat, S. and Zabczyk, J., Stochastic Partial Differential Equations with Lèvy Noise, Cambridge: Cambridge Univ. Press, 2007.
[21] Ren, L., Zhou, Q. and Chen, L., Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with poission jumps and infinite delay, J. Optim. Theory Appl., 2011, 149: 315-331.
[22] Taniguchi, T. and Luo, J.W., The existence and asymptotic behaviour of mild solutions for stochastic evolution equations with infinite delays driven by Poisson jumps, Stoch. Dyn., 2009, 9(2): 217-229.
[23] Tudor, C., Almost periodic solutions of affine stochastic evolution equations, Stoch. Stoch. Rep., 1992, 38: 251-266.
[24] Wang, Y. and Liu, Z.X., Almost periodic solutions for stochastic differential equations with Lèvy noise, Nonlinearity, 2012, 25: 2803-2821.
[25] Zhao, Z.H., Chang, Y.K. and Li, W.S., Asymptotically almost periodic, almost periodic and pseudo almost periodic mild solutions for neutral differential equations, Nonlinear Anal. Real World Appl., 2010, 11: 3037-3044.
[1] 董一林. Lévy过程驱动的带局部Lipschitz系数的随机微分方程解的遍历性[J]. 数学进展, 2018, 47(1): 11-30.
[2] 张伟年. 广义指数二分性与微分方程的不变流形[J]. 数学进展, 1993, 22(1): 1-45.
Full text



首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录

© 2015-2017 北京大学图书馆 .