## Journal of the Mathematical Society of Japan

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

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

#### 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 in Project Euclid: 9 February 2009

**Permanent link to this document**

https://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. J. Math. Soc. Japan 61 (2009), no. 1, 263--289. doi:10.2969/jmsj/06110263. https://projecteuclid.org/euclid.jmsj/1234189036.