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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 \cite{Kiu80}, following some ideas in \cite{Chybiryakov} 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.
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Dates and versions

hal-00639336 , version 1 (08-11-2011)

Identifiers

  • HAL Id : hal-00639336 , version 1

Cite

Loïc Chaumont, Henry Pantí, Víctor Manuel Rivero. The Lamperti representation of real-valued self-similar Markov processes. 2011. ⟨hal-00639336⟩
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