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Volume 42, Issue 6
Wong-Zakai Approximations for Stochastic Volterra Equations

Jie Xu & Mingbo Zhang

DOI: 10.4208/jcm.2305-m2022-0268

J. Comp. Math., 42 (2024), pp. 1526-1553.

Published online: 2024-11

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  • Abstract

In this paper, we shall prove a Wong-Zakai approximation for stochastic Volterra equations under appropriate assumptions. We may apply it to a class of stochastic differential equations with the kernel of fractional Brownian motion with Hurst parameter $H ∈ (1/2, 1)$ and subfractional Brownian motion with Hurst parameter $H ∈ (1/2, 1).$ As far as we know, this is the first result on stochastic Volterra equations in this topic.

  • Keywords

Stochastic Volterra equations, Wong-Zakai approximations, Fractional Brownian motion, Subfractional Brownian motion, Quadratic mean convergence.

  • AMS Subject Headings

60H10, 60H07

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-42-1526, author = {Xu , Jie and Zhang , Mingbo}, title = {Wong-Zakai Approximations for Stochastic Volterra Equations}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {6}, pages = {1526--1553}, abstract = {

In this paper, we shall prove a Wong-Zakai approximation for stochastic Volterra equations under appropriate assumptions. We may apply it to a class of stochastic differential equations with the kernel of fractional Brownian motion with Hurst parameter $H ∈ (1/2, 1)$ and subfractional Brownian motion with Hurst parameter $H ∈ (1/2, 1).$ As far as we know, this is the first result on stochastic Volterra equations in this topic.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2305-m2022-0268}, url = {http://global-sci.org/intro/article_detail/jcm/23506.html} }
TY - JOUR T1 - Wong-Zakai Approximations for Stochastic Volterra Equations AU - Xu , Jie AU - Zhang , Mingbo JO - Journal of Computational Mathematics VL - 6 SP - 1526 EP - 1553 PY - 2024 DA - 2024/11 SN - 42 DO - http://doi.org/10.4208/jcm.2305-m2022-0268 UR - https://global-sci.org/intro/article_detail/jcm/23506.html KW - Stochastic Volterra equations, Wong-Zakai approximations, Fractional Brownian motion, Subfractional Brownian motion, Quadratic mean convergence. AB -

In this paper, we shall prove a Wong-Zakai approximation for stochastic Volterra equations under appropriate assumptions. We may apply it to a class of stochastic differential equations with the kernel of fractional Brownian motion with Hurst parameter $H ∈ (1/2, 1)$ and subfractional Brownian motion with Hurst parameter $H ∈ (1/2, 1).$ As far as we know, this is the first result on stochastic Volterra equations in this topic.

Xu , Jie and Zhang , Mingbo. (2024). Wong-Zakai Approximations for Stochastic Volterra Equations. Journal of Computational Mathematics. 42 (6). 1526-1553. doi:10.4208/jcm.2305-m2022-0268
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