Stopped Brownian-increment tamed Euler method

TL;DR

This paper introduces a novel explicit Euler-type method for SDEs that replaces Brownian increments with bounded functions, achieving strong convergence under specific growth conditions.

Contribution

It presents a new tamed Euler method with proven strong convergence rate one-half for SDEs with polynomial coefficients and controlled growth conditions.

Findings

Achieves strong convergence rate 0.5 for a broad class of SDEs.

Handles SDEs with polynomial coefficients and logarithmic growth in local monotonicity.

Provides theoretical proof of convergence under specified conditions.

Abstract

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.