分数布朗运动驱动的带脉冲的中立性随机泛函微分方程的渐近稳定性

Abstract

CLC Number:

O211.9

Jing Cui,Qiuju Liang,Nana Bi. Asymptotic Stability of Impulsive Neutral Stochastic Functional Differential Equation Driven by Fractional Brownian Motion[J].Acta mathematica scientia,Series A, 2019, 39(3): 570-581.

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References 26

1	Maslowski B , Nualart D . Evolution equations driven by a fractional Brownian motion. J Funct Anal, 2003, 110: 277- 305
2	Boufoussi B , Hajji S . Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space. Statist Probab Lett, 2011, 82 (8): 1549- 1558
3	Boufoussi B , Hajji S . Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motion. Statist Probab Lett, 2017, 129: 222- 229 doi: 10.1016/j.spl.2017.06.006
4	Feyel D , Pradelle A de la . On fractional Brownian processes. Potential Anal, 1999, 10: 273- 288 doi: 10.1023/A:1008630211913
5	Nualart D . The Malliavin Calculus and Related Topics. Berlin: Springer-Verlag, 2006
6	Ruan D H , Luo J W . Fixed points and exponential stability of stochastic functional partial differential equations driven by fractional Brownian motion. Publ Math Debrecen, 2015, 86: 285- 293
7	Prato G Da , Zabczyk J . Stochastic Equations in Infinite Dimensions. Cambridge: Cambridge Univ Press, 1992
8	Arthi G , Park Ju H , Jung H Y . Existence and exponential stability for neutral stochastic integrodifferential equations with impulses driven by a fractional Brownian motion. Commun Nonlinear Sci Numer Simul, 2016, 32: 145- 157 doi: 10.1016/j.cnsns.2015.08.014
9	Cui J , Yan L , Sun X . Exponential stability for neutral stochastic partial differential equations with delays and Poisson Jumps. Statist Probab Lett, 2011, 81: 1970- 1977 doi: 10.1016/j.spl.2011.08.010
10	Luo J W . Stability of stochastic partial differential equations with infinite delays. J Comput Appl Math, 2008b, 222: 364- 371 doi: 10.1016/j.cam.2007.11.002
11	Acquistapace P , Terreni B . A unified approach to abstract linear nonautonomous parabolic equations. Rend Sem Mat Univ Padova, 1987, 78: 47- 107
12	Acquistapace P , Terreni B . Initial boundary value problems and optimal control for nonautonomous parabolic systems. SIAM J Control Optim, 1991, 29: 89- 118 doi: 10.1137/0329005
13	Sakthivel R , Luo J W . Asymptotic stability of impulsive stochastic partial differential equations with infinite delays. J Math Anal Appl, 2009, 356: 1- 6 doi: 10.1016/j.jmaa.2009.02.002
14	Caraballo T , Liu K . Exponential stability of mild solutions of stochastic partial differential equations with delays. Stoch Anal Appl, 1999, 17: 743- 763 doi: 10.1080/07362999908809633
15	Caraballo T , Garrido-Atienza M J , Taniguchi T . The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion. Nonlinear Anal, 2011, 74: 3671- 3684 doi: 10.1016/j.na.2011.02.047
16	Caraballo T , Mamadou A D . Asymptotic stability of neutral stochastic functional integro-differential equations. Electron Commun Probab, 2015, 20 (1): 1- 13
17	Caraballo T , Garrido-Atienza Mar'a J , Jos'e Real . Asymptotic Stability of Nonlinear Stochastic Evolution Equations. Stoch Anal Appl, 2003, 21 (2): 301- 327 doi: 10.1081/SAP-120019288
18	Duncan T E , Maslowski B , Pasik-Duncan B . Fractional Brownian motion and stochastic equations in Hilbert spaces. Stoch Dyn, 2002, 2: 225- 250 doi: 10.1142/S0219493702000340
19	Duc L H , Garrido-Atienzac M J . Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in ($\frac{1}{2}$, 1). J Differential Equations, 2018, 264: 1119- 1145 doi: 10.1016/j.jde.2017.09.033
20	Taniguchi T , Liu K , Truman A . Existence, uniqueness and asymptotic behavior of mild solutions to stochastic functional differential equations in Hilbert spaces. J Differential Equations, 2002, 181: 72- 91 doi: 10.1006/jdeq.2001.4073
21	Mao X . Stochastic Differential Equations and Applications. Chichester, UK: Horwood Publishing, 1997
22	Ren Y , Cheng X , Sakthivel R . On time-dependent stochastic evolution equations driven by fractional Brownian motion in Hilbert space with finite delay. Math Method Appl Sci, 2013, 37: 2177- 2184
23	Ren Y , Cheng X , Sakthivel R . Impulsive neutral stochastic functional integro-differential equations with infinite delay driven by fBm. Appl Math Comput, 2014, 247: 205- 212
24	Revathib P , Sakthivel R , Ren Y . Stochastic functional differential equations of Sobolev-type with infinite delay. Statist Probab Lett, 2016, 109: 68- 77 doi: 10.1016/j.spl.2015.10.019
25	Bahuguna D , Sakthivel R , Chadha A . Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with infinite delay. Stoch Anal Appl, 2017, 39: 63- 88
26	Ren Y , Hou T , Sakthivel R . Non-densely defined impulsive neutral stochastic functional differential equations driven by fBm in Hilbert space with infinite delay. Front Math China, 2015, 10: 351- 365 doi: 10.1007/s11464-015-0392-z

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Asymptotic Stability of Impulsive Neutral Stochastic Functional Differential Equation Driven by Fractional Brownian Motion

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