Bernoulli

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

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

Loïc Chaumont, Henry Pantí, and Víctor Rivero

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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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1386078611

Digital Object Identifier
doi:10.3150/12-BEJ460

Mathematical Reviews number (MathSciNet)
MR3160562

Zentralblatt MATH identifier
1284.60077

Keywords
Lamperti representation Lévy processes multiplicative invariant processes self-similar Markov processes

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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