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Generalised liouville processes and their properties

Part of: Stochastic analysis Stochastic processes Markov processes

Published online by Cambridge University Press:  23 November 2020

Edward Hoyle  and
Levent Ali Menguturk Open the ORCID record for Levent Ali Menguturk [Opens in a new window]
Edward Hoyle*
Affiliation:
AHL Partners LLP
Levent Ali Menguturk*
Affiliation:
University College London
*
*Postal address: AHL Partners LLP, Man Group plc, London EC4R 3AD, UK.
**Postal address: Department of Mathematics, University College London, London WC1E 6BT, UK.
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Abstract

We define a new family of multivariate stochastic processes over a finite time horizon that we call generalised Liouville processes (GLPs). GLPs are Markov processes constructed by splitting Lévy random bridges into non-overlapping subprocesses via time changes. We show that the terminal values and the increments of GLPs have generalised multivariate Liouville distributions, justifying their name. We provide various other properties of GLPs and some examples.

Keywords

Lévy processLévy bridgeMarkov processmultivariate Liouville distribution

MSC classification

Primary: 60G20: Generalized stochastic processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60H05: Stochastic integrals
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1088 - 1110
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Copyright
© Applied Probability Trust 2020

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