Convergence, Non-negativity and Stability of a New Tamed Euler–Maruyama Scheme for Stochastic Differential Equations with Hölder Continuous Diffusion Coefficient
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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.
KeywordsExponential stability Hölder continuous diffusion Non-negativity Stochastic differential equation Tamed Euler–Maruyama approximation
Mathematics Subject Classification (2010)65C30 65L20 60H10
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.