Convergence Analysis of the Balanced Implicit Method 
for the Wright-Fisher Model with No Drift

Yaqi An; Jianguo Tan

doi:https://doi.org/10.14445/22315373/IJMTT-V70I11P107

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 70 | Issue 11 | Year 2024 | Article Id. IJMTT-V70I11P107 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I11P107

Convergence Analysis of the Balanced Implicit Method for the Wright-Fisher Model with No Drift

Yaqi An, Jianguo Tan

Received	Revised	Accepted	Published
01 Oct 2024	04 Nov 2024	19 Nov 2024	30 Nov 2024

Citation :

Yaqi An, Jianguo Tan, "Convergence Analysis of the Balanced Implicit Method for the Wright-Fisher Model with No Drift," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 11, pp. 45-50, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I11P107

Abstract

In this paper, we discuss the Balanced Implicit Method (BIM) of the Wright-Fisher model, and the convergence of this method for the Wright-Fisher model with no drift is proved in 𝐿1sense. Finally, we give an example to illustrate the convergence of the BIM. The numerical experiment shows that the convergence order is 1 2 theoretical results.

Keywords

Balanced implicit method, Numerical solution, Stochastic differential equation, Strong convergence, Wright-Fisher model.

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