Modelling with stochastic differential equations

In this thesis subject of modelling real life problems with random differential equations and Ito stochastic differential equations are considered. For this purpose, necessary mathematical fundementals for theory of stochastic differential equations are given. Moreover, for two real life problems stochastic differential equation models are constructed and solved .First of all, a radioactive decay problem is modelled by a random differential equation and a solution of this model is obtained. Then some inferences about the solution are made and obtained results are illustrated with tables and figures.Secondly, after introduction of Samuelson model for stock prices, in this work a particular stochastic differential equation model is constructed for stock prices via modelling procedure given in literature. To compare both models for estimation of stock prices, daily closing prices of MOTOROLA stock between 20.03.09-11.05.09 are investigated. Parameters are estimated for both models via programs written with MATLAB. Then obtained models are solved numerically and calculated estimations are illustrated with tables and figures. It should be noted that Samuelson model provides better estimations when it?s compared to the model suggested in this work.