Metody diskretizace stochastických modelů se spojitým časem

Abstract

This thesis deals with the discretization of stochastic differential equations, which are used to model dynamical systems affected by random disturbances. While the model is formulated in continuous time, practical applications require its transformation into a discrete-time form. The aim of this thesis is to present the basic theory of stochastic differential equations and to analyze methods of their discretization. The Wiener process, the Itô integral, and Itô’s formula are introduced. For linear systems with constant coefficients, an exact discrete-time model is presented. In the nonlinear case, the Euler–Maruyama method and its convergence are discussed. The results are illustrated by the example of geometric Brownian motion.