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2006 Infinitely Divisible Random Probability Distributions with an Application to a Random Motion in a Random Environment
Tokuzo Shiga, Hiroshi Tanaka
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Electron. J. Probab. 11: 1144-1183 (2006). DOI: 10.1214/EJP.v11-380

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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Tokuzo Shiga. Hiroshi Tanaka. "Infinitely Divisible Random Probability Distributions with an Application to a Random Motion in a Random Environment." Electron. J. Probab. 11 1144 - 1183, 2006. https://doi.org/10.1214/EJP.v11-380

Information

Accepted: 7 December 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1127.60051
MathSciNet: MR2268541
Digital Object Identifier: 10.1214/EJP.v11-380

Subjects:
Primary: 60K37
Secondary: 60E07 , 60G09 , 60G57

Keywords: Infinite divisibility , Lévy-Itô représentation , Lévy-Khintchin representation , random environment , random probability distribution

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