Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior

References

[1] T. Bojdecki, L. G. Gorostiza and A. Talarczyk, Sub-fractional Brownian motion and its relation to occupation times, Statist. Probab. Lett. 69 (2004), no. 4, 405–419. 10.1016/j.spl.2004.06.035Suche in Google Scholar

[2] T. Caraballo and M. A. Diop, Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion, Front. Math. China 8 (2013), no. 4, 745–760. 10.1007/s11464-013-0300-3Suche in Google Scholar

[3] T. Caraballo, M. A. Diop and A. A. Ndiaye, Asymptotic behavior of neutral stochastic partial functional integro-differential equations driven by a fractional Brownian motion, J. Nonlinear Sci. Appl. 7 (2014), no. 6, 407–421. 10.22436/jnsa.007.06.04Suche in Google Scholar

[4] T. Caraballo, M. A. Diop and A. A. Ndiaye, Existence results for time-dependent stochastic neutral functional integrodifferential equations driven by a fractional Brownian motion, J. Numer. Math. Stoch. 6 (2014), no. 1, 84–99. Suche in Google Scholar

[5] T. Caraballo, M. J. Garrido-Atienza and T. Taniguchi, The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion, Nonlinear Anal. 74 (2011), no. 11, 3671–3684. 10.1016/j.na.2011.02.047Suche in Google Scholar

[6] Y.-K. Chang and J. J. Nieto, Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators, Numer. Funct. Anal. Optim. 30 (2009), no. 3–4, 227–244. 10.1080/01630560902841146Suche in Google Scholar

[7] M. Dieye, M. A. Diop and K. Ezzinbi, On exponential stability of mild solutions for some stochastics partial integrodifferential equations., Statist. Probab. Lett. 123 (2017), 61–76. 10.1016/j.spl.2016.10.031Suche in Google Scholar

[8] M. A. Diop and T. Caraballo, Asymptotic stability of neutral stochastic functional integro-differential equations, Electron. Commun. Probab. 20 (2015), Paper No. 1. 10.1214/ECP.v19-3036Suche in Google Scholar

[9] M. A. Diop, T. Caraballo and A. A. Ndiaye, Exponential behavior of solutions to stochastic integrodifferential equations with distributed delays, Stoch. Anal. Appl. 33 (2015), no. 3, 399–412. 10.1080/07362994.2014.1000070Suche in Google Scholar

[10] M. A. Diop, K. Ezzinbi and M. Lo, Existence and uniqueness of mild solutions to some neutral stochastic partial functional integrodifferential equations with non-Lipschitz coefficients, Int. J. Math. Math. Sci. 2012 (2012), Article ID 748590. 10.1155/2012/748590Suche in Google Scholar

[11] M. A. Diop, K. Ezzinbi and M. Lo, Mild solution of neutral stochastic partial functional integrodifferential equations with non-Lipschitz coefficients, Afr. Mat. 24 (2013), no. 4, 671–682. 10.1007/s13370-012-0089-3Suche in Google Scholar

[12] M. A. Diop, K. Ezzinbi and M. Lo, Asymptotic stability of impulsive stochastic partial integrodifferential equations with delays, Stochastics 86 (2014), no. 4, 696–706. 10.1080/17442508.2013.879143Suche in Google Scholar

[13] M. A. Diop, K. Ezzinbi and M. Lo, Existence and exponential stability for some stochastic neutral partial functional integrodifferential equations, Random Oper. Stoch. Equ. 22 (2014), no. 2, 73–83. 10.1515/rose-2014-0008Suche in Google Scholar

[14] K. Dzhaparidze and H. van Zanten, A series expansion of fractional Brownian motion, Probab. Theory Related Fields 130 (2004), no. 1, 39–55. 10.1007/s00440-003-0310-2Suche in Google Scholar

[15] R. C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc. 273 (1982), no. 1, 333–349. 10.1090/S0002-9947-1982-0664046-4Suche in Google Scholar

[16] I. Mendy, Parametric estimation for sub-fractional Ornstein–Uhlenbeck process, J. Statist. Plann. Inference 143 (2013), no. 4, 663–674. 10.1016/j.jspi.2012.10.013Suche in Google Scholar

[17] D. Nualart, The Malliavin Calculus and Related Topics, 2nd ed., Probab. Appl. (N. Y.), Springer, Berlin, 2006. Suche in Google Scholar

[18] J. Prüss, Evolutionary Integral Equations and Applications, Mod. Birkhäuser Class., Birkhäuser/Springer, Basel, 1993. 10.1007/978-3-0348-8570-6Suche in Google Scholar

[19] R. Ravi Kumar, Nonlocal Cauchy problem for analytic resolvent integrodifferential equations in Banach spaces, Appl. Math. Comput. 204 (2008), no. 1, 352–362. 10.1016/j.amc.2008.06.050Suche in Google Scholar

[20] C. Tudor, Some properties of the sub-fractional Brownian motion, Stochastics 79 (2007), no. 5, 431–448. 10.1080/17442500601100331Suche in Google Scholar

[21] C. Tudor, Berry–Esséen bounds and almost sure CLT for the quadratic variation of the sub-fractional Brownian motion, J. Math. Anal. Appl. 375 (2011), no. 2, 667–676. 10.1016/j.jmaa.2010.10.002Suche in Google Scholar

[22] J. Wu, Theory and Applications of Partial Functional-Differential Equations, Appl. Math. Sci. 119, Springer, New York, 1996. 10.1007/978-1-4612-4050-1Suche in Google Scholar