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Convergence, Non-negativity and Stability of a New Tamed Euler–Maruyama Scheme for Stochastic Differential Equations with Hölder Continuous Diffusion Coefficient

  • Trung-Thuy Kieu
  • Duc-Trong Luong
  • Hoang-Long NgoEmail author
  • Thu-Thuy Nguyen
Original Article
  • 12 Downloads

Abstract

We propose and analyze a new tamed Euler–Maruyama approximation scheme for stochastic differential equations with Hölder continuous diffusion. This new scheme preserves the stability and non-negativity of the exact solution.

Keywords

Exponential stability Hölder continuous diffusion Non-negativity Stochastic differential equation Tamed Euler–Maruyama approximation 

Mathematics Subject Classification (2010)

65C30 65L20 60H10 

Notes

Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2017.316. The paper was completed during a scientific stay of the third author at the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose hospitality is gratefully appreciated.

The authors thank the anonymous referees and Dai Taguchi for their valuable suggestions and comments.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationCau GiayVietnam

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