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Estimate of transition kernel for Euler-Maruyama scheme for SDEs driven by alpha-stable noise and applications

Xing Huang, Yongqiang Suo, Chenggui Yuan Orcid Logo

Numerical Algorithms

Swansea University Author: Chenggui Yuan Orcid Logo

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Abstract

In this paper, the discrete parametrix method is adopted to investigate the estimation of transition kernel for Euler-Maruyama scheme SDEs driven by α-stable noise, which implies Krylov’s estimate and Khasminskii’s estimate. As an application, the convergence rate of Euler-Maruyama scheme for a clas...

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Published in: Numerical Algorithms
ISSN: 1017-1398 1572-9265
Published: Springer Science and Business Media LLC
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URI: https://cronfa.swan.ac.uk/Record/cronfa63548
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Abstract: In this paper, the discrete parametrix method is adopted to investigate the estimation of transition kernel for Euler-Maruyama scheme SDEs driven by α-stable noise, which implies Krylov’s estimate and Khasminskii’s estimate. As an application, the convergence rate of Euler-Maruyama scheme for a class of multidimensional SDEs with singular drift (by the use of Zvonkin’s transformation) is obtained.
Keywords: Zvonkin’s transformation, Euler-Maruyama scheme, Transition kernel, Krylov’s estimate
College: Faculty of Science and Engineering