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arXiv · 0909.1331

Fluctuations of Multi-Dimensional Kingman-LÉvy Processes

Thu Nguyen
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Abstract

In the recent paper \cite{Ng5} we have introduced a method of studying the multi-dimensional Kingman convolutions and their associated stochastic processes by embedding them into some multi-dimensional ordinary convolutions which allows to study multi-dimensional Bessel processes in terms of the cooresponding Brownian motions. Our further aim in this paper is to introduce k-dimensional Kingman-Lévy (KL) processes and prove some of their fluctuation properties which are analoguous to that of k-symmetric Lévy processes. In particular, the Lévy-Itô decomposition and the series representation of Rosiński type for k-dimensional KL-processes are obtained.

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Thu Nguyen. 2009-09-07. Fluctuations of Multi-Dimensional Kingman-LÉvy Processes. https://arxiv.org/abs/0909.1331

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