## Bernoulli

• Bernoulli
• Volume 19, Number 5B (2013), 2494-2523.

### The Lamperti representation of real-valued self-similar Markov processes

#### Abstract

In this paper, we obtain a Lamperti type representation for real-valued self-similar Markov processes, killed at their hitting time of zero. Namely, we represent real-valued self-similar Markov processes as time changed multiplicative invariant processes. Doing so, we complete Kiu’s work [Stochastic Process. Appl. 10 (1980) 183–191], following some ideas in Chybiryakov [Stochastic Process. Appl. 116 (2006) 857–872] in order to characterize the underlying processes in this representation. We provide some examples where the characteristics of the underlying processes can be computed explicitly.

#### Article information

Source
Bernoulli, Volume 19, Number 5B (2013), 2494-2523.

Dates
First available in Project Euclid: 3 December 2013

https://projecteuclid.org/euclid.bj/1386078611

Digital Object Identifier
doi:10.3150/12-BEJ460

Mathematical Reviews number (MathSciNet)
MR3160562

Zentralblatt MATH identifier
1284.60077

#### Citation

Chaumont, Loïc; Pantí, Henry; Rivero, Víctor. The Lamperti representation of real-valued self-similar Markov processes. Bernoulli 19 (2013), no. 5B, 2494--2523. doi:10.3150/12-BEJ460. https://projecteuclid.org/euclid.bj/1386078611

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