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Volume 16, Issue 4
Discretization of Jump Stochastic Differential Equations in Terms of Multiple Stochastic Integrals

Chunwah Li, Shengchang Wu & Xiaoqing Liu

J. Comp. Math., 16 (1998), pp. 375-384.

Published online: 1998-08

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  • Abstract

In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to approximate these multiple stochastic integrals by converting them into systems of simple SDEs and solving the systems by lower order numerical schemes. The reliability of this approach is clarified in theory and demonstrated in numerical examples. In consequence, the results are applied to the strong discretization of both continuous and jump SDEs.

  • Keywords

Brownian motion, Poisson process, stochastic differential equation, multiple stochastic integral, strong discretization.

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COPYRIGHT: © Global Science Press

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@Article{JCM-16-375, author = {Li , ChunwahWu , Shengchang and Liu , Xiaoqing}, title = {Discretization of Jump Stochastic Differential Equations in Terms of Multiple Stochastic Integrals}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {4}, pages = {375--384}, abstract = {

In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to approximate these multiple stochastic integrals by converting them into systems of simple SDEs and solving the systems by lower order numerical schemes. The reliability of this approach is clarified in theory and demonstrated in numerical examples. In consequence, the results are applied to the strong discretization of both continuous and jump SDEs.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9168.html} }
TY - JOUR T1 - Discretization of Jump Stochastic Differential Equations in Terms of Multiple Stochastic Integrals AU - Li , Chunwah AU - Wu , Shengchang AU - Liu , Xiaoqing JO - Journal of Computational Mathematics VL - 4 SP - 375 EP - 384 PY - 1998 DA - 1998/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9168.html KW - Brownian motion, Poisson process, stochastic differential equation, multiple stochastic integral, strong discretization. AB -

In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to approximate these multiple stochastic integrals by converting them into systems of simple SDEs and solving the systems by lower order numerical schemes. The reliability of this approach is clarified in theory and demonstrated in numerical examples. In consequence, the results are applied to the strong discretization of both continuous and jump SDEs.

Li , ChunwahWu , Shengchang and Liu , Xiaoqing. (1998). Discretization of Jump Stochastic Differential Equations in Terms of Multiple Stochastic Integrals. Journal of Computational Mathematics. 16 (4). 375-384. doi:
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