Infinitely Divisible Random Probability Distributions with an Application to a Random Motion in a Random Environment

Abstract

The infinite divisibility of probability distributions on the space $P (R )$ of probability distributions on $R$ is defined and related fundamental results such as the Levy-Khintchin formula, representation of Ito type of infinitely divisible RPD, stable RPD and Levy processes on $P (R )$ are obtained. As an application we investigate limiting behaviors of a simple model of a particle motion in a random environment