Modeling of systems using Itô's stochastic differential equations

This paper deals with the modeling of systems subject to random perturbations. The main objective is to compare the experimentally measured trajectories with the solutions of the ordinary diferential equation (ODE) and the stochastic dierential equation (SDE) which model the systems analyzed with the purpose of verify if the SDEs capture the random perturbations and therefore, are more appropriate to describe the phenomena with random noise. To this end,the Ito’s calculus is used and numerical simulations of the SDEs are done in MATLAB using the Euler-Maruyama method. As an application of the SDEs, an optimal investment problem is solved in analytic form by following the standard dynamic programming technique.

Keywords: Brownian motion, Ito's calculus, Optimal control, Stochastic processes, White noise.