Generating the Underlying Process of the Forward Kolmogorov Equations

Abstract

This paper deals with the numerical solution of the forward kolmogorov equations problem, in addition to, the use of the Markov Chain Monte Carlo simulation technique for generating the underlying process of these equations and to predict the sample path behavior of this process. As an illustration of the use of this approach, numerical and numerical simulation results are obtained when the underlying process is of Poisson type and Continuous Time Markov Chain type. We obvious from the results we obtained the efficiency of Monte Carlo Markov chain simulation technique to predict sample path of these processes through out extended time periods.