Have a personal or library account? Click to login
A note on almost sure exponential stability of θ-Euler-Maruyama approximation for neutral stochastic differential equations with time-dependent delay when θ ∈ (


12
{1 \over 2}

, 1) Cover

A note on almost sure exponential stability of θ-Euler-Maruyama approximation for neutral stochastic differential equations with time-dependent delay when θ ∈ ( 12 {1 \over 2} , 1)

Open Access
|Oct 2024

References

  1. M. Jovanović, S. Janković, Neutral stochastic functional differential equations with additive pertubations, Appl. Math. Comput. 213 (2009) 370–379.
  2. G. Lan, C. Yuan, Exponential stability of the exact solutions and θ–EM approximations to neutral SDDEs with Markov switching, J. Comput. Appl. Math. 285 (2015) 230-242.
  3. Q. Luo, X. Mao, Y. Shen, New criteria on exponential stability of neutral stochastic differential delay equations, Systems and Control Letters 55 (2006) 826–834.
  4. X. Mao, M. J. Rassias, Khasminskii-type theorems for stochastic differential delay equations, Stochastic analysis and applications (2005) 1045–1069.
  5. X. Mao, Stochastics differential equations and their applications, Horwood Publishing Limited, 1997.
  6. X. Mao, Asymptotic properties of neutral stochastic differential delay equations, Stochastics and Stochastics Reports 68 (2000) 273–295.
  7. X. Mao, Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions, Appl. Math. Comput. 217 (2011) 5512–5524.
  8. X. Mao, L. Szpruch, Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients, J. Comput. Appl. Math. 238 (2013) 14–28.
  9. M. Milošević, M. Jovanović, S. Janković, An approximate method via Taylor series for stochastic differential equations, J. Math. Anal. Appl. 363 (2010) 128–137.
  10. M. Milošević, M. Jovanović, An application of Taylor series in the approximation of solutions to stochastic differential equations with time- dependent delay, J. Comput. Appl. Math. 235 (2011) 4439–4451.
  11. M. Milošević, Highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama method, Mathematical and Computer Modelling 54 (2011) 2235–2251.
  12. M. Milošević, Almost sure exponential stability of solutions to highly nonlinear neutral stochastics differential equations with time-dependent delay and Euler-Maruyama approximation, Mathematical and Computer Modelling 57 (2013) 887–899.
  13. M. Milošević, Implicit numerical methods for highly nonlinear neutral stochastics differential equations with time-dependent delay, Appl. Math. and Comput. 244 (2014) 741–760.
  14. M. Obradović, M. Milošević, Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler-Maruyama method, J. Comput. Appl. Math. 309 (2017) 244–266.
  15. [15] M. Obradović, M. Milošević, Almost sure exponential stability of the θ- Euler-Maruyama method for neutral stochastic differential equations with time-dependent delay when θ ∈ [0, 12 {1 \over 2} ], Filomat 31:18 (2017) 5629-5645.
  16. [16] M. Obradović, M. Milošević, Almost sure exponential stability of the θ-Euler-Maruyama method, when θ ∈ ( 12 {1 \over 2} , 1), for neutral stochastic differential equations with time-dependent delay under nonlinear growth conditions, Calcolo 56:9 (2019).
  17. M. Obradović, Implicit numerical methods for neutral stochastic differential equations with unbounded delay and Markovian switching. Appl. Math. Comput. 347 (2019) 664-687.
  18. A. N. Shiryaev, Probability, Springer, Berlin, 1996.
  19. L. Tan, C. Yuan, Convergence rates of theta-method for NSDDEs under non-globally Lipschitz continuous coefficients, Bulletin of Mathematical Sciences, 09 (03), (2019) 1950006 (32 pages).
  20. F. Wu, X. Mao, L. Szpruch, Almost sure exonential stability of numerical solutions for stochastic delay differential equations, Numer. Math. 115 (2010) 681–697.
  21. M. Xue, S. Zhou, S. Hu, Stability of nonlinear neutral stochastic functional differential equations, J. Appl. Math. Volume 2010, Article ID 425762, 26 pages doi:10.1155/2010/425762
  22. Z. Yan, A. Xiao, X. Tang, Strong convergence of the split-step theta method for neutral stochastic delay differential equations, Applied Numerical Mathematics 120 (2017) 215–232.
  23. Z. Yu, Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations, Abstract and Applied Analysis (2011) doi:10.1155/2011/14079.
  24. J. Zhao, Y. Yi, Y. Xu, Strong convergence and stability of the split- step theta method for highly nonlinear neutral stochastic delay integro- differential equation, Applied Numerical Mathematics 157 (2020) 385–404.
DOI: https://doi.org/10.2478/auom-2024-0032 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 125 - 148
Submitted on: Sep 12, 2023
Accepted on: Dec 20, 2023
Published on: Oct 17, 2024
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 Maja Obradović, Marija Milošević, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.