Fractional Poisson fields and martingales

Aletti, Giacamo, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Merzbach, Ely 2018. Fractional Poisson fields and martingales. Journal of Statistical Physics 170 (4) , pp. 700-730. 10.1007/s10955-018-1951-y

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Abstract

We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Springer
ISSN:	0022-4715
Date of First Compliant Deposit:	6 January 2018
Date of Acceptance:	3 January 2018
Last Modified:	22 Nov 2024 14:30
URI:	https://orca.cardiff.ac.uk/id/eprint/107943

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