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Volume 42, Issue 4
Convergence of Modified Truncated Euler-Maruyama Method for Stochastic Differential Equations with Hölder Diffusion Coefficients

Guangqiang Lan & Yu Jiang

DOI: 10.4208/jcm.2302-m2022-0246

J. Comp. Math., 42 (2024), pp. 1109-1123.

Published online: 2024-04

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  • Abstract

Convergence of modified truncated Euler-Maruyama (MTEM) method for stochastic differential equations (SDEs) with $(1/2 + α)$-Hölder continuous diffusion coefficients are investigated in this paper. We prove that the MTEM method for SDE converges to the exact solution in $L^q$ sense under given conditions. Two examples are provided to support our conclusions.

  • Keywords

Stochastic differential equations, Modified truncated Euler-Maruyama method, Strong convergence, One-sided Lipschitz, Hölder continuous.

  • AMS Subject Headings

65C30, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-1109, author = {Lan , Guangqiang and Jiang , Yu}, title = {Convergence of Modified Truncated Euler-Maruyama Method for Stochastic Differential Equations with Hölder Diffusion Coefficients}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {4}, pages = {1109--1123}, abstract = {

Convergence of modified truncated Euler-Maruyama (MTEM) method for stochastic differential equations (SDEs) with $(1/2 + α)$-Hölder continuous diffusion coefficients are investigated in this paper. We prove that the MTEM method for SDE converges to the exact solution in $L^q$ sense under given conditions. Two examples are provided to support our conclusions.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2302-m2022-0246}, url = {http://global-sci.org/intro/article_detail/jcm/23048.html} }
TY - JOUR T1 - Convergence of Modified Truncated Euler-Maruyama Method for Stochastic Differential Equations with Hölder Diffusion Coefficients AU - Lan , Guangqiang AU - Jiang , Yu JO - Journal of Computational Mathematics VL - 4 SP - 1109 EP - 1123 PY - 2024 DA - 2024/04 SN - 42 DO - http://doi.org/10.4208/jcm.2302-m2022-0246 UR - https://global-sci.org/intro/article_detail/jcm/23048.html KW - Stochastic differential equations, Modified truncated Euler-Maruyama method, Strong convergence, One-sided Lipschitz, Hölder continuous. AB -

Convergence of modified truncated Euler-Maruyama (MTEM) method for stochastic differential equations (SDEs) with $(1/2 + α)$-Hölder continuous diffusion coefficients are investigated in this paper. We prove that the MTEM method for SDE converges to the exact solution in $L^q$ sense under given conditions. Two examples are provided to support our conclusions.

Guangqiang Lan & Yu Jiang. (2024). Convergence of Modified Truncated Euler-Maruyama Method for Stochastic Differential Equations with Hölder Diffusion Coefficients. Journal of Computational Mathematics. 42 (4). 1109-1123. doi:10.4208/jcm.2302-m2022-0246
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