Estimate of Heat Kernel for Euler-Maruyama Scheme of SDEs Driven by {\alpha}-Stable Noise and Applications

TL;DR

This paper analyzes the heat kernel estimation for Euler-Maruyama schemes of SDEs driven by alpha-stable noise, providing convergence rates for schemes with singular drifts using advanced probabilistic estimates.

Contribution

It introduces a discrete parameter expansion approach to estimate heat kernels for SDEs with alpha-stable noise and derives convergence rates for schemes with singular drifts.

Findings

Established krylov's and khasminskii's estimates for the scheme

Derived convergence rates for multidimensional SDEs with singular drifts

Applied Zvonkin's transformation in the analysis

Abstract

In this paper, the discrete parameter expansion is adopted to investigate the estimation of heat kernel for Euler-Maruyama scheme of SDEs driven by {\alpha}-stable noise, which implies krylov's estimate and khasminskii's estimate. As an application, the convergence rate of Euler-Maruyama scheme of a class of multidimensional SDEs with singular drift( in aid of Zvonkin's transformation) is obtained.