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Existence and Stability Results for Time-Dependent Impulsive Neutral Stochastic Partial Integrodifferential Equations with Rosenblatt Process and Poisson Jumps


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ANGURAJ, A.—VINODKUMAR, A.: Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays, Electronic Journal of Qualitive Theory of Differential Equations, 67 (2009), 1–13. Search in Google Scholar

LIN, A—REN, Y.—XIA, N.: On neutral impulsive stochastic integrodifferential equations with infinite delays via fractional operators, Math. Comput. Modelling 51 (2010), 413–424. Search in Google Scholar

CARABALLO, T.—GARRIDO-ATIENZA, T. M. J.—TANIGUCHI, T.: The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion, Nonlinear Anal. 74 (2011), 3671–3684. Search in Google Scholar

DIEYE, M.—DIOP, M. A.—EZZINBI, K.: On exponential stability of mild solutions for some stochastic partial integrodifferential equations. Statist. Probab. Lett. 123 (2017), 61–76 Search in Google Scholar

GRIMMER, R. C.: Resolvent operators for integral equations in a Banach space,Trans. Amer. Math. Soc. 273 (1982), 333–349. Search in Google Scholar

ANGURAJ, A.—RAVIKUMAR, K.: Existence and stability results for impulsive stochastic functional integrodifferential equations with Poisson jumps, Journal of Applied Nonlinear Dynamics, 8 (2019), no. 3, 407–417. Search in Google Scholar

BENCHOHRA, M.—OUAHAB, A.: Impulsive neutral functional differential equations with variable times, Nonlinear Anal. 55 (2003), no. 6, 679–693. Search in Google Scholar

BIAGINI, F.—HU, Y.—OKSENDAL, B.—ZHANG, T.: Stochastic Calculus for Fractional Brownian Motion and Application. Springer-Verlag, Berlin, 2008. Search in Google Scholar

BOUFOUSSI, B.—HAJJI, S.: Neutral stochastic functional differential equation ‘driven by a fractional Brownian motion in a Hilbert space, Statist. Probab. Lett. 82 (2012), 1549–1558. Search in Google Scholar

BOUFOUSSI, B.—HAJJI, S.: Functional differential equations in Hilbert space driven by a fractional Brownian motion,Afr. Mat. 23 (2011), no. 2, 173–194. Search in Google Scholar

BOUFOUSSI, B.—HAJJI, S.—LAKHEL, E.: Time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion, Communications on Stochastic Analysis 10 (2016), no. 1, DOI: 10.31390/cosa.10.1.01. Search in Google Scholar

BOUFOUSSI, B.—HAJJI, S.: Successive approximation of neutral functional stochastic differential equations with jumps,Sat.Proba. Lett. 80 (2010), 324–332. Search in Google Scholar

CARABALLO, T.—DIOP, M. A.—NDIAYE, A. A.: Asymptotic behaviour of neutral stochastic partial functional integrodifferential equations driven by a fraction Brownian motion, J. Nonlinear Sci. Appl. 7 (2014), 407–421. Search in Google Scholar

FEYEL, D.—DE LA PRADELLE, A.: On fractional Brownian processes, Potential Anal. 10 (1999), 273–288. Search in Google Scholar

LAKHEL, E.—HAJJI, S.: Existence and uniqueness of mild solutions to neutral stochastic functional differential equations driven by a fractional Brownian motion with non-Lipschitz coefficients, J. Number. Math. Stoch, 7 (2015), no. 1. 14–29. Search in Google Scholar

LAKSHMIKANTHAM, V.—BAINOV, D. D.—SIMEONOV, P. S.: Theory of Impulsive Differential Equations. In: Series in Modern Applied Mathematics Vol. 6, World Scientific Publishing Co., Inc., Teaneck, NJ, 1989. Search in Google Scholar

REN, Y.—CHENG, X.—SAKTHIVEL, R.: Impulsive neutral stochastic functional integrodifferential equations with infinite delay driven by fractional Brownian motion, Appl. Math. Comput 247 (2014), 205–212. Search in Google Scholar

XU, D.—YANG, Z.: Exponential stability of nonlinear impulsive neutral differential equations with delays, Nonlinear Anal, 67 (2006), no. 5, 1426–1439. Search in Google Scholar

DOBRUSHIN, R.L.— MAJOR, P.: Non-central limit theorems for non-linear functionals of Gaussian fields, Z. Wahrscheinlichkeitstheorie Verw. Geb. 50 (1979), 27–52. Search in Google Scholar

LUO, J.—TANIGUCHI, T.: The existence and uniqueness for non-lipschitz stochastic neutral delay evolution equations driven by Poisson jumps,Stoch.Dyn, 9 (2009), no. 1, 135–152. Search in Google Scholar

MANDELBROT, B.—NESS, V.: Fractional Brownian motion, fraction noises and applications,SIAM Reviews, 10 (1968), no. 4, 422–437. Search in Google Scholar

TAM, J. Q.—WANG, H. L.—GUO, Y. F.: Existence and uniqueness of solution to neutral stochastic functional differential equations with Poisson jumps, Abstr. Appl. Anal. (2012), 1-20 pp. Search in Google Scholar

CONT, R.—TANKOV, P.: Financial Modeling with jump processes. Financial Mathematics series, Chapman and Hall/CRC, Boca Raton, 2004. Search in Google Scholar

CUI, J.—YAN, T.: Successive approximation of neutral stochastic evolution equations with infinite delay and Poisson jumps, Appl. Math. Comp. 128 (2012), 6776–6784. Search in Google Scholar

HALE, J. K.—MEYER, K. R.: A class of functional equations of neutral type,Memoirs of the Amer. Math. Soc. 76 (1967), 1–65. Search in Google Scholar

HALE, J. K.—VERDUYN LUNEL, S. M.: Introduction to Functional Differential Equations. Springer-Verlag, New York, 1993. Search in Google Scholar

KOLMANOVSKII, V. B.—NOSOV, V. B.: Stability of neutral-type functional-differential equations, Nonlinear Anal. 6 (1982), 873–910. Search in Google Scholar

LAKHEL, EL H.—HAJJI, S.: Neutral stochastic functional differential equations driven by a fractional Brownian motion and Poisson point processes, Gulf Journal of Mathematics, 4 (2016), no. 3, 1–14, https://doi.org/10.56947/gjom.v4i3.69 Search in Google Scholar

TINDEL, S.—TUDOR, C. A.—VIENS, F.: Stochastic evolution equations with fractional Brownian motion, Probab Theory Related Fields 127 (2003), no. 2, 186–204. Search in Google Scholar

NUALART, D.: The Malliavin Calculus and Related Topics. 2nd ed. In: Probab. Appl. (NY). Springer, New York, 2006. Search in Google Scholar

KINGMAN, J. C. F.: Poisson Processes and Poisson Random Measure. Oxford Univ. Press, Oxford, 1993. Search in Google Scholar

LUO, J.—LIU, K.: Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps, Stochastic Process. Appl. 118 (2014), 864–895. Search in Google Scholar

TAQQU, M.: Weak convergence to the fractional Brownian motion and to the Rosenblatt process, Advances in Applied Probabilitz 7 (1975), no. 2, 249–249, DOI:10.2307/1426060. Search in Google Scholar

TINDEL,S.—TUDOR, CA. —VIENS, F.: Stochastic evolution equations with fractional Brownian motion, Probab. Theory Related Fields, 127 (2003), 186–204. Search in Google Scholar

LEONENKO, N.—AHN, V.: Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long-range dependence, Journal of Appl. Math. and Stochastic Anal. 14 (2001), 27–46. Search in Google Scholar

ABRY, P.—PIPIRAS, V.: Wavelet-based synthesis of the Rosenblatt process, Signal Processing 86 (2006), 2326–2339. Search in Google Scholar

byTudor, C. A. Analysis of the Rosenblatt process, ESAIM Probab. Stat. 12 (2008), 230–257. Search in Google Scholar

MAEJIMA, M.—TUDOR, CA: Wiener integrals with respect to the Hermite process and a non central limit theorem, Stoch. Anal. Appl. 25 (2007), 1043–1056. Search in Google Scholar

MAEJIMA, M.—TUDOR, CA: Selfsimilar processes with stationary increments in the second Wiener chaos, Probab. Math. Statist. 32 (2012), 167–186. Search in Google Scholar

MAEJIMA M.—TUDOR, CA: . On the distribution of the Rosenblatt process, Statist. Probab. Lett. 83 (2013) 1490–1495. Search in Google Scholar

PIPIRAS, V.— TAQQU, MS.: Regularization and integral representations of Hermite processes. Statist. Probab. Lett. 80 (2010), 2014–2023. Search in Google Scholar

KRUK, I.—RUSSO, F.—TUDOR, C. A.: Wiener integrals, Malliavin calculus and covariance measure structure, J. Funct. Anal. 249 (2007), 92–142. Search in Google Scholar

CHALISHAJAR, DIMPLEKUMAR N.: Controllability of second order impulsive neutral functional differential inclusions with infinite delay, J. Optim. Theory Appl. 154 (2012), 672–684. DOI: 10.1007/s10957-012-0025-6. Search in Google Scholar

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