Fractional Poisson Fields

Nikolai Leonenko, Ely Merzbach

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space. Some properties are given and, in particular, we prove a long-range dependence property.

Original languageEnglish
Pages (from-to)155-168
Number of pages14
JournalMethodology and Computing in Applied Probability
Volume17
Issue number1
DOIs
StatePublished - Mar 2013

Bibliographical note

Publisher Copyright:
© 2013, Springer Science+Business Media New York.

Funding

Nikolai Leonenko and Ely Merzbach were partially supported by a grant of the Commission of the European Communities PIRSES-GA-2008-230804 (Marie Curie) “Multi-parameter Multi-fractional Brownian Motion”.

FundersFunder number
European CommissionPIRSES-GA-2008-230804

    Keywords

    • Inverse subordinator
    • Long-range dependence
    • Poisson fields
    • Subordinator

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