Volume 10, Issue 4
Second-Order Methods for Solving Stochastic Differential Equations

J. Comp. Math., 10 (1992), pp. 376-387

Published online: 1992-10

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• Abstract

In this paper we discuss the numerical methods with second-order accuracy for solving stochastic differential equations. An unbiased sample approximation method for $I_n=\int ^{t_{n+1}}_{t_n}(B_u-B_{t_n})^2du$ is proposed, where {$B_u$} is a Brownian motion. Then second-order schemes are derived both for scalar cases and for system cases. The errors are measured in the mean square sense. Several numerical examples are included, and numerical results indicate that second-order schemes compare favorably with Euler's schemes and 1.5th-order schemes.

• Keywords

@Article{JCM-10-376, author = {}, title = {Second-Order Methods for Solving Stochastic Differential Equations}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {4}, pages = {376--387}, abstract = { In this paper we discuss the numerical methods with second-order accuracy for solving stochastic differential equations. An unbiased sample approximation method for $I_n=\int ^{t_{n+1}}_{t_n}(B_u-B_{t_n})^2du$ is proposed, where {$B_u$} is a Brownian motion. Then second-order schemes are derived both for scalar cases and for system cases. The errors are measured in the mean square sense. Several numerical examples are included, and numerical results indicate that second-order schemes compare favorably with Euler's schemes and 1.5th-order schemes. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9370.html} }
TY - JOUR T1 - Second-Order Methods for Solving Stochastic Differential Equations JO - Journal of Computational Mathematics VL - 4 SP - 376 EP - 387 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9370.html KW - AB - In this paper we discuss the numerical methods with second-order accuracy for solving stochastic differential equations. An unbiased sample approximation method for $I_n=\int ^{t_{n+1}}_{t_n}(B_u-B_{t_n})^2du$ is proposed, where {$B_u$} is a Brownian motion. Then second-order schemes are derived both for scalar cases and for system cases. The errors are measured in the mean square sense. Several numerical examples are included, and numerical results indicate that second-order schemes compare favorably with Euler's schemes and 1.5th-order schemes.