Advantages of using stochastic differential equations: Brownian bridge and geometric Brownian motion
Keywords:
Solution, Confidence, Simulation, Stochastic, Differential equationAbstract
This article exposes several advantages of using stochastic differential equations (SDE) compared to classical differential equations. It addresses the difference between the exponential growth model represented as a classical differential equation and its stochastic counterpart, known as geometric Brownian motion. Additionally, it analyzes the Brownian bridge as opposed to a straight line; the latter model is used in ecological contexts to simulate migratory trajectories as seen in Kranstauber, B., et al. (2012). The article begins with an explanation of the most relevant results from stochastic analysis, which is essential for developing a model based on an SDE. Subsequently, it proceeds to explain the simulation of these stochastic differential equations using the Euler-Maruyama method and the stochastic Runge-Kutta method. These simulations are crucial for generating confidence curves associated with the average function.
References
Kranstauber, B., Kays, R., LaPoint, S. D., Wikelski, M., & Safi, K. (2012). A dynamic Brownian bridge movement model to estimate utilization distributions for heterogeneous animal movement. Journal of Animal Ecology, 81(4), 738-746.
Exarchos, I., & Theodorou, E. A. (2018). Stochastic optimal control via forward and backward stochastic differential equations and importance sampling. Automatica, 87, 159-165.
Suescun D, D., Ule D, G., & Rojas A, O. (2021). Runge-Kutta implicit stochastic of order 1.5 applied to the equations of point kinetics.
Castañeda, L. B., Arunachalam, V., & Dharmaraja, S. (2012). Introduction to probability and stochastic processes with applications. John Wiley & Sons.
Rincón, L. (2006). Introducción a las ecuaciones diferenciales estocásticas. UNAM. México.
Resnick, S. (2019). A probability path. Springer.
Brown, R. (1828). XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. The philosophical magazine, 4(21), 161-173.
Soriano, A., & Loro, H. (2022). Un problema en Econofísica: Predicción de activos financieros mediante el Movimiento Browniano Geométrico, dentro del mercado bursátil.
Downloads
Additional Files
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Multidisciplinary & Health Education Journal
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.