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Infinitely divisible random probability distributions with an application to a random motion in a random environment. (English) Zbl 1127.60051

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

MSC:

60G57 Random measures
60G09 Exchangeability for stochastic processes
60E07 Infinitely divisible distributions; stable distributions
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