Advanced search
Publication Cover
Stochastic Analysis and Applications Volume 40, 2022 - Issue 4
Submit an article Journal homepage
286
Views
1
CrossRef citations to date
0
Altmetric
Articles

Tamed-adaptive Euler-Maruyama approximation for SDEs with locally Lipschitz continuous drift and locally Hölder continuous diffusion coefficients

Trung-Thuy KieuHanoi National University of Education, Cau Giay, Hanoi, VietnamView further author information
,
Duc-Trong LuongHanoi National University of Education, Cau Giay, Hanoi, VietnamView further author information
&
Hoang-Long NgoHanoi National University of Education, Cau Giay, Hanoi, VietnamCorrespondence[email protected]
View further author information
Pages 714-734 | Received 04 Jun 2020, Accepted 26 Jun 2021, Published online: 12 Aug 2021

References

  • Kloeden, P. E., Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. Applications of Mathematics (New York), Vol. 23. Berlin: Springer-Verlag.
  • Jeanblanc, M., Yor, M., Chesney, M. (2009). Mathematical Methods for Financial Markets. Springer Finance. London: Springer-Verlag.
  • Milstein, G. N., Tretyakov, M. V. (2004). Stochastic Numerics for Mathematical Physics. Scientific Computation. Berlin: Springer-Verlag.
  • Hutzenthaler, M., Jentzen, A., Kloeden, P. E. (2011). Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Proc. R Soc. A. 467(2130):1563–1576. DOI: https://doi.org/10.1098/rspa.2010.0348.
  • Hutzenthaler, M., Jentzen, A., Kloeden, P. E. (2012). Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Ann. Appl. Probab. 22(4):1611–1641. DOI: https://doi.org/10.1214/11-AAP803.
  • Hutzenthaler, M., Jentzen, A. (2020). On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients. Ann. Probab. 48(1):53–93. DOI: https://doi.org/10.1214/19-AOP1345.
  • Ngo, H.-L., Luong, D.-T. (2017). Strong rate of tamed Euler-Maruyama approximation for stochastic differential equations with Hölder continuous diffusion coefficient. Braz. J. Probab. Stat. 31(1):24–40. DOI: https://doi.org/10.1214/15-BJPS301.
  • Ngo, H. L., Luong, D. T. (2019). Tamed Euler-Maruyama approximation for stochastic differential equations with locally Hölder continuous diffusion coefficients. Statist. Probab. Lett. 145:133–140. DOI: https://doi.org/10.1016/j.spl.2018.09.006.
  • Sabanis, S. (2013). A note on tamed Euler approximations. Electron. Commun. Probab. 18:10. DOI: https://doi.org/10.1214/ECP.v18-2824.
  • Sabanis, S. (2016). Euler approximations with varying coefficients: The case of superlinearly growing diffusion coefficients. Ann. Appl. Probab. 26(4):2083–2105. DOI: https://doi.org/10.1214/15-AAP1140.
  • Fang, W., Giles, M. B. (2020). Adaptive Euler-Maruyama method for SDEs with nonglobally Lipschitz drift. Ann. Appl. Probab. 30(2):526–560. DOI: https://doi.org/10.1214/19-AAP1507.
  • Li, X. M. X., Yang, H. (2020). Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations. arXiv preprint:2002.06756.
  • Gyöngy, I., Rásonyi, M. (2011). A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients. Stoch. Process. Appl. 121(10):2189–2200. DOI: https://doi.org/10.1016/j.spa.2011.06.008.
  • Ngo, H.-L., Taguchi, D. (2015). Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients. Math. Comp. 85(300):1793–1819. DOI: https://doi.org/10.1090/mcom3042.
  • Yamada, T., Watanabe, S. (1971). On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11:155–167.
  • Fischer, M., Nappo, G. (2009). On the moments of the modulus of continuity of Itô processes. Stoch. Anal. Appl. 28(1):103–122. DOI: https://doi.org/10.1080/07362990903415825.
  • Revuz, D., Yor, M. (1999). Continuous Martingales and Brownian Motion. Grundlehren Der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Vol. 293, 3rd ed. Berlin: Springer-Verlag.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.