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), 61–76Search 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.v4i3.69Search 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