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

By L. Chaumont, Henry Pant'i, V. Rivero. 2011

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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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Management Information Systems

View Paper: https://www.semanticscholar.org/paper/b4fdd7d0539fca62326c66f1f83b093b20f6118a