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

Xing Huang; Yongqiang Suo; Chenggui Yuan

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arXiv · 2103.01323

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

Xing Huang·Yongqiang Suo·Chenggui Yuan

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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.

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Xing Huang, Yongqiang Suo, Chenggui Yuan. 2021-03-01. Estimate of Heat Kernel for Euler-Maruyama Scheme of SDEs Driven by {\alpha}-Stable Noise and Applications. https://arxiv.org/abs/2103.01323

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