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.
Keywords
Cite
@article{arxiv.1111.1272,
title = {The Lamperti representation of real-valued self-similar Markov processes},
author = {Loïc Chaumont and Henry Pantí and Víctor Rivero},
journal= {arXiv preprint arXiv:1111.1272},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.3150/12-BEJ460 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)