Volume 12, Issue 3
Analysis and Numerical Approximation for a Nonlinear Hidden-Memory Variable-Order Fractional Stochastic Differential Equation

Jinhong Jia, Zhiwei Yang, Xiangcheng Zheng & Hong Wang

East Asian J. Appl. Math., 12 (2022), pp. 673-695.

Published online: 2022-04

Export citation
  • Abstract

We prove the well-posedness of a nonlinear hidden-memory variable-order fractional stochastic differential equation driven by a multiplicative white noise, in which the hidden-memory type variable order describes the memory of a fractional order. We then present a Euler-Maruyama scheme for the proposed model and prove its strong convergence rate. Numerical experiments are performed to substantiate the theoretical results.

  • Keywords

Variable-order fractional stochastic differential equation, hidden memory, Euler-Maruyama method, strong convergence.

  • AMS Subject Headings

60H20, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-12-673, author = {}, title = {Analysis and Numerical Approximation for a Nonlinear Hidden-Memory Variable-Order Fractional Stochastic Differential Equation }, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {3}, pages = {673--695}, abstract = {

We prove the well-posedness of a nonlinear hidden-memory variable-order fractional stochastic differential equation driven by a multiplicative white noise, in which the hidden-memory type variable order describes the memory of a fractional order. We then present a Euler-Maruyama scheme for the proposed model and prove its strong convergence rate. Numerical experiments are performed to substantiate the theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.311021.220222}, url = {http://global-sci.org/intro/article_detail/eajam/20413.html} }
TY - JOUR T1 - Analysis and Numerical Approximation for a Nonlinear Hidden-Memory Variable-Order Fractional Stochastic Differential Equation JO - East Asian Journal on Applied Mathematics VL - 3 SP - 673 EP - 695 PY - 2022 DA - 2022/04 SN - 12 DO - http://doi.org/10.4208/eajam.311021.220222 UR - https://global-sci.org/intro/article_detail/eajam/20413.html KW - Variable-order fractional stochastic differential equation, hidden memory, Euler-Maruyama method, strong convergence. AB -

We prove the well-posedness of a nonlinear hidden-memory variable-order fractional stochastic differential equation driven by a multiplicative white noise, in which the hidden-memory type variable order describes the memory of a fractional order. We then present a Euler-Maruyama scheme for the proposed model and prove its strong convergence rate. Numerical experiments are performed to substantiate the theoretical results.

Jinhong Jia, Zhiwei Yang, Xiangcheng Zheng & Hong Wang. (2022). Analysis and Numerical Approximation for a Nonlinear Hidden-Memory Variable-Order Fractional Stochastic Differential Equation . East Asian Journal on Applied Mathematics. 12 (3). 673-695. doi:10.4208/eajam.311021.220222
Copy to clipboard
The citation has been copied to your clipboard