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

Tokuzo Shiga (Tokyo Institute of Technology)
Hiroshi Tanaka (Keio University)

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

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Pages: 1144-1183

Publication Date: December 7, 2006

DOI: 10.1214/EJP.v11-380

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