New criteria for exponential stability in mean square of stochastic functional differential equations with infinite delay

Pham Huu Anh Ngoc

doi:10.3934/eect.2021040

Article Contents

2022, Volume 11, Issue 4: 1191-1200. Doi: 10.3934/eect.2021040

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New criteria for exponential stability in mean square of stochastic functional differential equations with infinite delay

Pham Huu Anh Ngoc^,

Vietnam National University-HCMC, Department of Mathematics, International University, Thu Duc city, Ho Chi Minh city, Vietnam

Corresponding author: Pham Huu Anh Ngoc
Corresponding author: Pham Huu Anh Ngoc

Received: November 2020

Revised: May 2021

Early access: August 2021

Published: August 2022

This work was supported by the Vietnam National University, Ho Chi Minh city under Grant B 2021-28-01/HD-KHCN

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Abstract

Stochastic functional differential equations with infinite delay are considered. A novel approach to exponential stability of such equations is proposed. New criteria for the mean square exponential stability of general stochastic functional differential equations with infinite delay are presented. Illustrative examples are given.

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Mathematics Subject Classification: Primary: 34D20; Secondary: 93E15.

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[1]	P. Guo and C. J. Li, Razumikhin-type theorems on the moment stability of the exact and numerical solutions for the stochastic pantograph differential equations, Journal of Computational and Applied Mathematics, 355 (2019), 77-909. doi: 10.1016/j.cam.2019.01.011.
[2]	J. Kato, Stability problem in functional differential equations with infinite delay, Funkcialaj Ekvacioj, 21 (1978), 63-80.
[3]	R. Khasminskii, Stochastic Stability of Differential Equations, With contributions by G. N. Milstein and M. B. Nevelson. Completely revised and enlarged second edition. Stochastic Modelling and Applied Probability, 66. Springer, Heidelberg, 2012. doi: 10.1007/978-3-642-23280-0.
[4]	J. Lei and M. C. Mackey, Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system, SIAM Journal on Applied Mathematics, 67 (2006/07), 387-407. doi: 10.1137/060650234.
[5]	X. Li and X. Fu, Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks, Journal of Computational and Applied Mathematics, 234 (2010), 407-417. doi: 10.1016/j.cam.2009.12.033.
[6]	Q. Li, Q. Zhang and B. Cao, Mean-square stability of stochastic age-dependent delay population systems with jumps, Acta Mathematicae Applicatae Sinica, English Series, 34 (2018), 145-154. doi: 10.1007/s10255-018-0732-3.
[7]	X. Mao, Razumikhin-type theorems on exponential stability of stochastic functional differential equations, Stochastic Process. Appl., 65 (1996), 233-250. doi: 10.1016/S0304-4149(96)00109-3.
[8]	X. Mao, Stochastic Differential Equations and Applications, Elsevier, New York, 2007.
[9]	P. H. A. Ngoc, Explicit criteria for mean square exponential stability of stochastic differential equations, Applied Mathematics Letters, 93 (2019), 22-28. doi: 10.1016/j.aml.2019.01.014.
[10]	P. H. A. Ngoc and T. T. Anh, Stability of nonlinear Volterra equations and applications, Applied Mathematics and Computation, 341 (2019), 1-14. doi: 10.1016/j.amc.2018.07.027.
[11]	P. H. A. Ngoc, Novel criteria for exponential stability in mean square of stochastic functional differential equations, Proceedings of the American Mathematical Society, 148 (2020), 3427-3436. doi: 10.1090/proc/14994.
[12]	P. H. A. Ngoc and L. T. Hieu, A novel approach to mean square exponential stability of stochastic delay differential equations, IEEE Transactions on Automatic Control, 66 (2021), 2351-2356. doi: 10.1109/TAC.2020.3005587.
[13]	G. Pavlovic and S. Jankovi, Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay, Journal of Computational and Applied Mathematics, 236 (2012), 1679-1690. doi: 10.1016/j.cam.2011.09.045.
[14]	W. Rudin, Real and Complex Analysis, 2$^nd$ edition. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1974.
[15]	L. Shaikhet, Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, Springer, Cham, 2013. doi: 10.1007/978-3-319-00101-2.
[16]	Z. Yang, E. Zhu, Y. Xu and Y. Tan, Razumikhin-type theorems on exponential stability of stochastic functional differential equations with infinite delay, Acta Appl. Math., 111 (2010), 219-231. doi: 10.1007/s10440-009-9542-1.
[17]	F. Wei and K. Wang, The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay, Journal of Mathematical Analysis and Applications, 331 (2007), 516-531. doi: 10.1016/j.jmaa.2006.09.020.
[18]	F. Wu and S. Hu, Razumikhin-type theorems on general decay stability and robustness for stochastic functional differential equations, International Journal of Robust and Nonlinear Control, 22 (2012), 763-777. doi: 10.1002/rnc.1726.
[19]	X. Zhao and F. Deng, New-type stability theorem for stochastic functional differential equations with application to SFDSs with distributed delays, International Journal of Systems Science, 45 (2014), 1156-1169. doi: 10.1080/00207721.2012.745028.
[20]	X. Zhao and F. Deng, New type of stability criteria for stochastic functional differential equations via Lyapunov functions, SIAM J. Control Optim., 52 (2014), 2319-2347. doi: 10.1137/130948203.
[21]	X. Zong, G. Yin, L. Y. Wang, T. Li and J. Zhang, Stability of stochastic functional differential systems using degenerate Lyapunov functionals and applications, Automatica J. IFAC, 91 (2018), 197-207. doi: 10.1016/j.automatica.2018.01.038.
[22]	S. Zhou, Z. Wang and D. Feng, Stochastic functional differential equations with infinite delay, Journal of Mathematical Analysis and Applications, 357 (2009), 416-426. doi: 10.1016/j.jmaa.2009.04.015.