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

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

2011-11-05

arxiv.org/abs/1111.1272v2

Mathematics

Probability

Scientific paper

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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