- Volume 19, Number 5B (2013), 2494-2523.
The Lamperti representation of real-valued self-similar Markov processes
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.
Bernoulli, Volume 19, Number 5B (2013), 2494-2523.
First available in Project Euclid: 3 December 2013
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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