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

Abstract

We propose a tamed-adaptive Euler-Maruyama approximation scheme for stochastic differential equations with locally Lipschitz continuous, polynomial growth drift, and locally Hölder continuous, polynomial growth diffusion coefficients. We consider the strong convergence and the stability of the new scheme. In particular, we show that under some sufficient conditions for the stability of the exact solution, the tamed-adaptive scheme converges strongly in both finite and infinite time intervals.

Keywords:

• Euler-Maruyama approximation
• Hölder continuous diffusion
• strong approximation
• polynomial growth coefficient

Acknowledgment

The authors would like to thank the referees for their useful comments and suggestions.

Additional information

Funding

Kieu Trung Thuy was funded by Vingroup Joint Stock Company and supported by the Domestic Master/PhD Scholarship Programme of Vingroup Innovation Foundation (VINIF), Vingroup Big Data Institute (VINBIGDATA), code VINIF.2020.TS.97. Luong Duc Trong was supported by a research grant from the Hanoi National University of Education.