پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 705 |
| تعداد مقالات | 10,157 |
| تعداد مشاهده مقاله | 71,530,024 |
| تعداد دریافت فایل اصل مقاله | 63,238,467 |
Qualitative behaviour of local non-Lipschitz stochastic integrodifferential system with Rosenblatt process and infinite delay | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 5، دوره 15، شماره 12، اسفند 2024، صفحه 45-58 اصل مقاله (457.74 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29778.4255 | ||
| نویسندگان | ||
| Essozimna Kpizim1؛ Ramkumar Kasinathan2؛ Ravikumar Kasinathan3؛ Khalil Ezzinbi4؛ Mamadou Abdoul Diop* 1 | ||
| 1Numerical Analysis and Computer Science Laboratory, Department of Mathematics, Gaston Berger University of Saint-Louis, UFR SAT, B.P:234, Saint-Louis, Senegal | ||
| 2Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 046, India | ||
| 3Department of Mathematics, PSG college of Arts and Science, Coimbatore, 641 014, India | ||
| 4Universit´e Cadi Ayyad, Facult´e des Sciences Semlalia D´epartement de Math´ematiques B.P. 2390 Marrakech, Morocco | ||
| تاریخ دریافت: 10 بهمن 1401، تاریخ پذیرش: 05 آذر 1402 | ||
| چکیده | ||
| The objective of this paper is to investigate the existence and uniqueness of mild solutions for stochastic integrodifferential evolution equations in Hilbert spaces with infinite delay and a Rosenblatt Process. The main results of this discussion are provided by Grimmer's resolvent operator theory and stochastic analysis. The theory is demonstrated with an example. | ||
| کلیدواژهها | ||
| $C_0$-semigroup؛ Grimmer resolvent operator؛ stochastic functional integrodifferential equations؛ Rosenblatt process | ||
| مراجع | ||
|
[1] B. Bayour and D.F.M. Torres, Existence of solution to a local fractional nonlinear differential equation, J. Comput. Appl. Math. 312 (2017), 127–133. [2] B. Boufoussi and S. Hajji, Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space, Statist. Probab. Lett. 82 (2012), 1549–1558. [3] 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.: Theory Meth. Appl. 74 (2011), no. 11, 3671–3684. [4] T. Caraballo, C. Ogouyandjou, F.K. Allognissode, and M.A. Diop, Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process, Discrete Continuous Dyn. Syst.-B 25 (2020), no. 2, 507. [5] J. Deng and S. Wang, Existence of solutions of nonlocal Cauchy problem for some fractional abstract differential equation, Appl. Math. Lett. 55 (2016), 42–48. [6] K. Dhanalakshmi and P. Balasubramaniam, Stability result of higher-order fractional neutral stochastic differential system with infinite delay driven by Poisson jumps and Rosenblatt process, Stochastic Anal. Appl. 38 (2020), no. 2, 352—372. [7] 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), 73–83. [8] R. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc. 273 (1982), no. 1, 333–349. [9] E. Hernandez, Existence results for partial neutral functional integrodifferential equations with unbounded delay, J. Math. Anal. Appl. 292 (2004), 194–210. [10] N.N. Leonenko and V.V. Anh, Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long-range dependence, J. Appl. Math. Stoch. Anal. 14 (2001), no. 1, 27–46. [11] M. Maejima and C.A. Tudor, Selfsimilar processes with stationary increments in the second wiener chaos, Probab. Math. Statist. 32 (2012), no. 1, 167–186. [12] B. Maslowski and J. Pospisil Ergodicity and, and parameter estimates for infinite-dimensional fractional Ornstein-Uhlenbeck process, Appl. Math. Optim. 57 (2008), 401–429. [13] B. Maslowski and D. Nualart, Evolution equations driven by a fractional Brownian motion, J. Funct. Anal. 202 (2003), 277-–305. [14] J.Y. Park, K. Balachandran, and N. Annapoorani, Existence results for impulsive neutral functional integrodifferential equations with infinite delay, Nonlinear Anal. 71 (2009), 3152–3162. [15] C. Parthasarathy, A. Vinodkumar, and M. Mallika Arjunan, and Uniqueness and existence, and stability of neutral stochastic functional integro-differential evolution with infinite delay, Int. J. Comput. Appl. 65 (2013), no. 15, 0975–8887. [16] K. Ramkumar, A.A. Gbaguidi, C. Ogouyandjou, and M. A. Diop, Existence and uniqueness of mild solutions of stochastic partial integro-differential impulsive equations with infinite delay via resolvent operator, Adv. Dyn. Syst. Appl. 14 (2019), no. 1, 83–118. [17] Y. Ren, X. Cheng, and R. Sakthivel, On time-dependent stochastic evolution equations driven by fractional Brownian motion in a Hilbert space with finite delay, Math. Meth. Appl. Sci. 37 (2014), no. 14, 2177–2184. [18] M. Rosenblatt, Independence and dependence, Proc. 4th Berkeley Symp. Math. Statist. Prob., 1961, pp. 431–443. [19] G.J. Shen and Y. Ren, Neutral stochastic partial differential equations with delay driven by Rosenblatt process in a Hilbert space, J. Korean Statist. Soc.44 (2015), 123–133. [20] G.J. Shen, Y. Ren, and Li M. Controllability and, and stability of fractional stochastic functional systems driven by Rosenblatt process, Collect. Math. 71 (2020), 63–82. [21] T. Taniguchi, Successive approximations to solutions of stochastic differential equations, J. Differ. Equ. 96 (1992), 152–169. [22] T. Taniguchi, The existence and uniqueness of energy solutions to local non-Lipschitz stochastic evolution equations, J. Math. Anal. Appl. 360 (2009), 245–253. [23] M. Taqqu, Weak convergence to fractional Brownian motion and to the Rosenblatt process, Adv. Appl. Probab. 7 (1975), no. 2, 249–249. [24] C.A. Tudor, Analysis of the Rosenblatt process, ESAIM: Probab. Statist. 12 (2008), 230–257. | ||
|
آمار تعداد مشاهده مقاله: 1,802 تعداد دریافت فایل اصل مقاله: 1,109 |
||