Numerical implementation of a stochastic differential equation of motion

Abstract

Using the ordinary differential equation of motion it is possible to determine the position in time of a mass that moves because it is disturbed by some deterministic action. For this work it was proposed to model a mass supporting a random disturbance. To do this, it was required to model Brownian motion since it efficiently represents the randomness of the phenomenon. Using the fundamentals of Functional Analysis, Probability Theory and Stochastic Processes, a stochastic differential equation of motion was obtained. In order to extract solutions from this equation, the Euler-Maruyama method was used, which was implemented computationally. The results obtained showed that the use of a non-deterministic version to model movement generates satisfactory results and of interest to science.

Keywords

• stochastic processes
• probability
• brownian motion
• stochastic differential equation
• euler-maruyama method