The logarithmic truncated EM method with weaker conditions

Abstract

In 2014, Neuenkirch and Szpruch established the drift-implicit Euler-Maruyama method for a class of SDEs which take values in a given domain. However, expensive computational cost is required for implementation of an implicit numerical method. A competitive positivity preserving explicit numerical method for SDEs which take values in the positive domain is the logarithmic truncated Euler-Maruyama method. However, assumptions for the logarithmic truncated Euler-Maruyama method used in previous work are restrictive which exclude some important SDE models with specific parameters. The main aim of this paper is to use weaker assumptions to establish strong convergence theory for the logarithmic truncated Euler-Maruyama method.