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Abstract
Since the seminal work of Lamperti, there is a lot of interest in the understanding of the general structure of selfsimilar Markov processes. Lamperti gave a representation of positive selfsimilar Markov processes with initial condition strictly larger than 0 which subsequently was extended to zero initial condition. For real selfsimilar Markov processes (rssMps), there is a generalization of Lamperti's representation giving a onetoone 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 selfsimilar Markov processes issued from the origin. The construction gives a pathwise representation through twosided Markov additive processes extending the Lamperti Kiu representation to the origin.
Original language  English 

Pages (fromto)  19522003 
Number of pages  52 
Journal  Annals of Probability 
Volume  45 
Issue number  3 
Early online date  15 May 2017 
DOIs  
Publication status  Published  31 May 2017 
Keywords
 Fluctuation theory
 Markov additive process
 Selfsimilar process
ASJC Scopus subject areas
 Statistics and Probability
 Statistics, Probability and Uncertainty
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 2 Finished

Self Similarity and Stable Processes
Kyprianou, A.
Engineering and Physical Sciences Research Council
1/10/14 → 30/03/16
Project: Research council

RealValued SelfSimilar Markov Processes and their Applications
Kyprianou, A.
Engineering and Physical Sciences Research Council
2/06/14 → 1/10/17
Project: Research council