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Real self-similar processes started from the origin

    1. [1] University of Mannheim

      University of Mannheim

      Stadtkreis Mannheim, Alemania

    2. [2] University of Bath

      University of Bath

      Reino Unido

    3. [3] Universität Münster
  • Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 3, 2017, págs. 1952-2003
  • Idioma: inglés
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  • Resumen
    • Since the seminal work of Lamperti, there is a lot of interest in the understanding of the general structure of self-similar Markov processes. Lamperti gave a representation of positive self-similar Markov processes with initial condition strictly larger than 00 which subsequently was extended to zero initial condition.

      For real self-similar Markov processes (rssMps), there is a generalization of Lamperti’s representation giving a one-to-one correspondence between Markov additive processes and rssMps with initial condition different from the origin.

      We develop fluctuation theory for Markov additive processes and use Kuznetsov measures to construct the law of transient real self-similar Markov processes issued from the origin. The construction gives a pathwise representation through two-sided Markov additive processes extending the Lamperti–Kiu representation to the origin.


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