In this article we propose a new explicit Euler-type approximation method for stochastic differential equations (SDEs). In this method, Brownian increments in the recursion of the Euler method are replaced by suitable bounded functions of the Brownian increments. We prove strong convergence rate one-half for a large class of SDEs with polynomial coefficient functions whose local monotonicity constant grows at most like the logarithm of a Lyapunov-type function.

翻译：在本篇文章中,我们提出了一种新的明确处理不同方程式的Euler型近似法(SDEs),在这种方法中,用适当的布朗加量的结合功能取代Euler法循环法中的Brownian增量。对于具有多数值系数功能的一大批SDE,我们证明我们强烈的趋同率是一半,这些功能的本地单数常数最多增长,就像Lyapunov型函数的对数一样。