A New Approach for Capturing the Probability Density Function of the Maximum Value of a Markov Process

Abstract

In the present paper a method to determine the probability distribution of the maximum value process (MVP) of a Markov process is proposed. In this method, an augmented vector process of a physical process and its MVP is constructed. The joint probability density function is then calculated by the path integral solution (PIS), and further the probability density function of the MVP can be obtained as the marginal probability density. A numerical example is shown to validate the proposed method.