MULTIVARIATE FRACTIONAL POISSON PROCESSES AND COMPOUND SUMS

被引：12

作者：

Beghin, Luisa ^{[1
,3
]}

Macci, Claudio ^{[2
,4
]}

机构：

[1] Sapienza Univ Roma, Rome, Italy

[2] Univ Roma Tor Vergata, I-00173 Rome, Italy

[3] Sapienza Univ Roma, Dipartimento Sci Stat, Piazzale Aldo Moro 5, I-00185 Rome, Italy

[4] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci, I-00133 Rome, Italy

来源：

ADVANCES IN APPLIED PROBABILITY | 2016年 / 48卷 / 03期

关键词：

Conditional independence; Fox-Wright function; fractional differential equation; random time-change;

D O I：

10.1017/apr.2016.23

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (nonfractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.

引用

页码：691 / 711

页数：21

共 22 条

[1]

[Anonymous], 2006, THEORY APPL FRACTION

[2]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[3]

[Anonymous], 2013, Cambridge Studies in Advanced Mathematics

[4]

[Anonymous], 2009, Levy processes and stochastic calculus

[5] Poisson-type processes governed by fractional and higher-order recursive differential equations [J].

Beghin, L. ;

Orsingher, E. .

ELECTRONIC JOURNAL OF PROBABILITY, 2010, 15 :684-709

[6] Fractional Poisson Processes and Related Planar Random Motions [J].

Beghin, L. ;

Orsingher, E. .

ELECTRONIC JOURNAL OF PROBABILITY, 2009, 14 :1790-1827

[7] Fractional Poisson process with random drift [J].

Beghin, Luisa ;

D'Ovidio, Mirko .

ELECTRONIC JOURNAL OF PROBABILITY, 2014, 19

[8]

Beghin L, 2014, J APPL PROBAB, V51, P19

[9]

Biard R, 2014, J APPL PROBAB, V51, P727

[10] FOKKER-PLANCK-KOLMOGOROV EQUATIONS ASSOCIATED WITH TIME-CHANGED FRACTIONAL BROWNIAN MOTION [J].

Hahn, Marjorie G. ;

Kobayashi, Kei ;

Umarov, Sabir .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139 (02) :691-705

← 1 2 3 →