Journal of the Mathematical Society of Japan

The Lévy-Itô decomposition of sample paths of Lévy processes with values in the space of probability measures

Kouji YAMAMURO

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Abstract

A definition of Lévy processes with values in the space of probability measures was introduced by Shiga and Tanaka (Electronic J. Prob. 11 (2006)). It is shown that the Lévy process with values in the space of probability measures in law has a modification satisfying a certain condition. The modification is a Lévy process in the sense of Shiga and Tanaka. The Lévy-Itô decomposition of sample paths of the Lévy process satisfying the condition is derived.

Article information

Source
J. Math. Soc. Japan Volume 61, Number 1 (2009), 263-289.

Dates
First available: 9 February 2009

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1234189036

Digital Object Identifier
doi:10.2969/jmsj/06110263

Mathematical Reviews number (MathSciNet)
MR2272879

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions

Keywords
Lévy-Itô decomposition Lévy process

Citation

YAMAMURO, Kouji. The Lévy-Itô decomposition of sample paths of Lévy processes with values in the space of probability measures. Journal of the Mathematical Society of Japan 61 (2009), no. 1, 263--289. doi:10.2969/jmsj/06110263. http://projecteuclid.org/euclid.jmsj/1234189036.


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