Fractional Poisson Fields and Martingales

Giacomo Aletti; Nikolai Leonenko; Ely Merzbach

doi:10.1007/s10955-018-1951-y

Fractional Poisson Fields and Martingales

Giacomo Aletti, Nikolai Leonenko, Ely Merzbach

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs 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.

Original language	English
Pages (from-to)	700-730
Number of pages	31
Journal	Journal of Statistical Physics
Volume	170
Issue number	4
DOIs	https://doi.org/10.1007/s10955-018-1951-y
State	Published - 1 Feb 2018

Keywords

Fractional Poisson fields
Fractional differential equations
Inverse subordinator
Martingale characterization
Second order statistics

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-018-1951-y

Cite this

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title = "Fractional Poisson Fields and Martingales",

abstract = "We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs 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.",

keywords = "Fractional Poisson fields, Fractional differential equations, Inverse subordinator, Martingale characterization, Second order statistics",

author = "Giacomo Aletti and Nikolai Leonenko and Ely Merzbach",

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doi = "10.1007/s10955-018-1951-y",

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TY - JOUR

T1 - Fractional Poisson Fields and Martingales

AU - Aletti, Giacomo

AU - Leonenko, Nikolai

AU - Merzbach, Ely

PY - 2018/2/1

Y1 - 2018/2/1

N2 - We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs 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.

AB - We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs 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.

KW - Fractional Poisson fields

KW - Fractional differential equations

KW - Inverse subordinator

KW - Martingale characterization

KW - Second order statistics

UR - http://www.scopus.com/inward/record.url?scp=85040950485&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-1951-y

DO - 10.1007/s10955-018-1951-y

M3 - مقالة

SN - 0022-4715

VL - 170

SP - 700

EP - 730

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 4

ER -

Fractional Poisson Fields and Martingales

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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