Numerical Solution of the Lotka-Volterra Stochastic Differential Equation
Keywords:
Stochastic differential equations, Lotka-Volterra model, Euler-Maruyama method, Milstein method
Abstract
This paper presents the modeling of the stochastic differential equation of Lotka-Volterra and introduces the application of two numerical methods to approximately obtain the solution to this stochastic model. The methods used to solve the stochastic differential equation are the Euler-Maruyama method and the Milstein method. Additionally, a methodology will be presented to obtain the parameters of the predator-prey model equation based on empirically obtained data from observations conducted over a fixed period of time.References
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control. SIAM Journal on Control and Optimization, 58(2), 735–754.
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9. Aplicadas, L. E. M. (2014). M´etodos num´ericos para la soluci´on de ecuaciones diferenciales estoc´asticas (Doctoral dissertation).
Benem´erita Universidad Aut´onoma De Puebla.
2. Øksendal, B., & Øksendal, B. (2003). Stochastic differential equations (pp. 65–84). Springer Berlin Heidelberg.
3. Hamza, K., & Klebaner, F. C. (2008). On the implicit Black–Scholes formula. Stochastics An International Journal of Probability and
Stochastic Processes, 80(1), 97–102.
4. Mikosch, T. (1998). Elementary stochastic calculus with finance in view. World Scientific.
5. Rinc´on, L. (2006). Introducci´on a las ecuaciones diferenciales estoc´asticas. UNAM. M´exico.
6. Hu, J., Liu, W., Deng, F., & Mao, X. (2020). Advances in stabilization of hybrid stochastic differential equations by delay feedback
control. SIAM Journal on Control and Optimization, 58(2), 735–754.
7. Platen, E., & Bruti-Liberati, N. (2010). Numerical solution of stochastic differential equations with jumps in finance (Vol. 64). Springer
Science & Business Media.
8. Gorham, J., Duncan, A. B., & Vollmer, S. J. (2019). The ANNALS. The Annals of Applied Probability, 29(5), 2613–3269.
9. Aplicadas, L. E. M. (2014). M´etodos num´ericos para la soluci´on de ecuaciones diferenciales estoc´asticas (Doctoral dissertation).
Benem´erita Universidad Aut´onoma De Puebla.
Published
2025-03-04
How to Cite
Cardona, E. M., Ramírez-Vanegas, C. A., & González Granada, J. R. (2025). Numerical Solution of the Lotka-Volterra Stochastic Differential Equation. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2307
Issue
Section
Research Articles
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