A note on tamed Euler approximations

TL;DR

This paper investigates the strong convergence of tamed Euler schemes for stochastic differential equations with superlinear drift, establishing classical convergence rates under certain Lipschitz conditions.

Contribution

It provides new strong convergence results for tamed Euler schemes with locally Lipschitz continuous coefficients and recovers the classical rate under stronger assumptions.

Findings

Strong convergence results for tamed Euler schemes with superlinear drift.

Classical convergence rate of 1/2 established under global Lipschitz conditions.

Extension of convergence analysis to locally Lipschitz continuous coefficients.

Abstract

Strong convergence results on tamed Euler schemes, which approximate stochastic differential equations with superlinearly growing drift coefficients that are locally one-sided Lipschitz continuous, are presented in this article. The diffusion coefficients are assumed to be locally Lipschitz continuous and have at most linear growth. Furthermore, the classical rate of convergence, i.e. one--half, for such schemes is recovered when the local Lipschitz continuity assumptions are replaced by global and, in addition, it is assumed that the drift coefficients satisfy polynomial Lipschitz continuity.