Strong convergence and temporal-spatial regularity for tamed Euler approximations of L\'evy-driven SDEs

TL;DR

This paper introduces a new tamed Euler scheme for Le9vy-driven SDEs with superlinear coefficients, proving its strong convergence and regularity properties, supported by numerical experiments.

Contribution

The paper presents a novel tamed Euler-type scheme for Le9vy-driven SDEs and establishes its strong convergence and regularity estimates, which were not previously available.

Findings

The scheme converges strongly to the true solution.

Temporal-spatial regularity estimates are derived.

Numerical experiments support theoretical results.

Abstract

We study the temporal-spatial regularity properties of tamed Euler approximations for L\'evy-driven SDEs with superlinearly growing drift and diffusion coefficients. We first introduce a novel tamed Euler-type scheme and establish its strong convergence. We then derive temporal-spatial regularity estimates with respect to the initial value, the initial time, and the evaluation time. In particular, we obtain a stability estimate for fixed step size and a corresponding continuity estimate in the vanishing step-size regime. Numerical experiments are presented to support the theoretical results.