Conditioned real self-similar Markov processes

Andreas E. Kyprianou, Victor Manuel Rivero Mercado, Weerapat Satitkanitkul

Resultado de la investigación: Contribución a una revistaArtículo

2 Citas (Scopus)

Resumen

In recent work, Chaumont et al. (2013) showed that is possible to condition a stable process with index α∈(1,2) to avoid the origin. Specifically, they describe a new Markov process which is the Doob h-transform of a stable process and which arises from a limiting procedure in which the stable process is conditioned to have avoided the origin at later and later times. A stable process is a particular example of a real self-similar Markov process (rssMp) and we develop the idea of such conditionings further to the class of rssMp. Under appropriate conditions, we show that the specific case of conditioning to avoid the origin corresponds to a classical Cramér–Esscher-type transform to the Markov Additive Process (MAP) that underlies the Lamperti–Kiu representation of a rssMp. In the same spirit, we show that the notion of conditioning a rssMp to continuously absorb at the origin also fits the same mathematical framework. In particular, we characterise the stable process conditioned to continuously absorb at the origin when α∈(0,1). Our results also complement related work for positive self-similar Markov processes in Chaumont and Rivero (2007).

Idioma originalInglés
Páginas (desde-hasta)954-977
Número de páginas24
PublicaciónStochastic Processes and their Applications
Volumen129
N.º3
DOI
EstadoPublicada - 1 mar 2019

Huella dactilar

Self-similar Processes
Stable Process
Markov Process
Markov processes
Conditioning
H-transform
Markov Additive Process
Complement
Limiting
Mathematical transformations
Transform

Citar esto

Kyprianou, Andreas E. ; Rivero Mercado, Victor Manuel ; Satitkanitkul, Weerapat. / Conditioned real self-similar Markov processes. En: Stochastic Processes and their Applications. 2019 ; Vol. 129, N.º 3. pp. 954-977.
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Conditioned real self-similar Markov processes. / Kyprianou, Andreas E.; Rivero Mercado, Victor Manuel; Satitkanitkul, Weerapat.

En: Stochastic Processes and their Applications, Vol. 129, N.º 3, 01.03.2019, p. 954-977.

Resultado de la investigación: Contribución a una revistaArtículo

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