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On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees

Abstract:

A Markov Additive Process is a bi-variate Markov process $(\xi,J)=\big((\xi_t,J_t),t\geq0\big)$ which should be thought of as a multi-type L\'evy process: the second component $J$ is a Markov chain on a finite space $\{1,\ldots,K\}$, and the first component $\xi$ behaves locally as a L\'evy process, with local dynamics depending on $J$. In the subordinator-like case where $\xi$ is nondecreasing, we establish several results concerning the moments of $\xi$ and of its exponential functional $I_...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Statistics
Role:
Author
ORCID:
0000-0003-1808-5105
Publisher:
Brazilian Institute for Pure and Applied Mathematics Publisher's website
Journal:
ALEA: Latin American Journal of Probability and Mathematical Statistics Journal website
Volume:
XV
Issue:
2
Pages:
1257-1292
Publication date:
2018-11-01
Acceptance date:
2018-10-03
ISSN:
1980-0436
Pubs id:
pubs:894399
URN:
uri:1dd2a90a-c346-4198-b625-42c095df8c5b
UUID:
uuid:1dd2a90a-c346-4198-b625-42c095df8c5b
Local pid:
pubs:894399
Keywords:

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