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Volume 8, Issue 6
Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps

Xu Yang & Weidong Zhao

DOI: 10.4208/aamm.2015.m1208

Adv. Appl. Math. Mech., 8 (2016), pp. 1004-1022.

Published online: 2018-05

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  • Abstract

In this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

  • Keywords

Split-step scheme, strong convergence, stochastic differential equation, jump-diffusion, one-side Lipschitz condition.

  • AMS Subject Headings

65C20, 60H35, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-1004, author = {Yang , Xu and Zhao , Weidong}, title = {Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {1004--1022}, abstract = {

In this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1208}, url = {http://global-sci.org/intro/article_detail/aamm/12128.html} }
TY - JOUR T1 - Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps AU - Yang , Xu AU - Zhao , Weidong JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1004 EP - 1022 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1208 UR - https://global-sci.org/intro/article_detail/aamm/12128.html KW - Split-step scheme, strong convergence, stochastic differential equation, jump-diffusion, one-side Lipschitz condition. AB -

In this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

Xu Yang & Weidong Zhao. (2020). Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps. Advances in Applied Mathematics and Mechanics. 8 (6). 1004-1022. doi:10.4208/aamm.2015.m1208
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