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 L'{e}vy-Khintchin formula, representation of It^{o} type of infinitely divisible RPD, stable RPD and L'{e}vy 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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