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

被引：0

作者：

Huang, Xing ^{[1
]}

Suo, Yongqiang ^{[2
]}

Yuan, Chenggui ^{[3
]}

机构：

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 211106, Peoples R China

[3] Swansea Univ, Dept Math, Bay Campus, Swansea SA1 8EN, Wales

来源：

NUMERICAL ALGORITHMS | 2023年 / 94卷 / 03期

关键词：

Zvonkin's transformation; Euler-Maruyama scheme; Transition kernel; Krylov's estimate; STOCHASTIC DIFFERENTIAL-EQUATIONS; MULTIDIMENSIONAL SDES; DEGENERATE SDES; SINGULAR DRIFT; CONVERGENCE;

D O I：

10.1007/s11075-023-01539-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the discrete parametrix method is adopted to investigate the estimation of transition kernel for Euler-Maruyama scheme SDEs driven by a-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.

引用

页码：1381 / 1402

页数：22

共 34 条

[1] Convergence rate of the EM algorithm for SDEs with low regular drifts [J].

Bao, Jianhai ;

Huang, Xing ;

Zhang, Shao-Qin .

JOURNAL OF APPLIED PROBABILITY, 2022, 59 (02) :447-470

[2] Convergence Rate of Euler-Maruyama Scheme for SDEs with Holder-Dini Continuous Drifts [J].

Bao, Jianhai ;

Huang, Xing ;

Yuan, Chenggui .

JOURNAL OF THEORETICAL PROBABILITY, 2019, 32 (02) :848-871

[3]

Blumenthal R.M., 1960, T AM MATH SOC, V95, P263, DOI [10.1090/S0002-9947-1960-0119247-6, 10.2307/1993291]

[4] Heat kernels for time-dependent non-symmetric stable-like operators [J].

Chen, Zhen-Qing ;

Zhang, Xicheng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 465 (01) :1-21

[5] Heat kernels and analyticity of non-symmetric jump diffusion semigroups [J].

Chen, Zhen-Qing ;

Zhang, Xicheng .

PROBABILITY THEORY AND RELATED FIELDS, 2016, 165 (1-2) :267-312

[6] ON TAMED EULER APPROXIMATIONS OF SDES DRIVEN BY LEVY NOISE WITH APPLICATIONS TO DELAY EQUATIONS [J].

Dareiotis, Konstantinos ;

Kumar, Chaman ;

Sabanis, Sotirios .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (03) :1840-1872

[7] Flow of diffeomorphisms for SDEs with unbounded Holder continuous drift [J].

Flandoli, F. ;

Gubinelli, M. ;

Priola, E. .

BULLETIN DES SCIENCES MATHEMATIQUES, 2010, 134 (04) :405-422

[8] The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate [J].

Goettlich, S. ;

Lux, K. ;

Neuenkirch, A. .

ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)

[9] On stochastic differential equations with locally unbounded drift [J].

Gyöngy, I ;

Martínez, T .

CZECHOSLOVAK MATHEMATICAL JOURNAL, 2001, 51 (04) :763-783

[10] A note on the Euler-Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient [J].

Halidias, Nikolaos ;

Kloeden, Peter E. .

BIT NUMERICAL MATHEMATICS, 2008, 48 (01) :51-59

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