On the convergence of quadratic variation for compound fractional poisson processes

Enrico Scalas; Noélia Viles

doi:10.2478/s13540-012-0023-2

On the convergence of quadratic variation for compound fractional poisson processes

Enrico Scalas
, Noélia Viles

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

The relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a stochastic process.

Lingua originale	Inglese
pagine (da-a)	314-331
Numero di pagine	18
Rivista	Fractional Calculus and Applied Analysis
Volume	15
Numero di pubblicazione	2
DOI	https://doi.org/10.2478/s13540-012-0023-2
Stato di pubblicazione	Pubblicato - giu 2012
Pubblicato esternamente	Sì

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10.2478/s13540-012-0023-2

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title = "On the convergence of quadratic variation for compound fractional poisson processes",

abstract = "The relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a stochastic process.",

keywords = "Compound renewal process, Continuous time random walk, Fractional Poisson process, Inverse stable subordinator, MWright functions, Mittag-Leffler waiting time, Quadratic variation",

author = "Enrico Scalas and No{\'e}lia Viles",

note = "Funding Information: This work was partially funded by MIUR Italian grant PRIN 2009 on Finitary and non-Finitary Probabilistic Methods in Economics within the project The Growth of Firms and Countries: Distributional Properties and Economic Determinants.",

year = "2012",

month = jun,

doi = "10.2478/s13540-012-0023-2",

language = "English",

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AU - Viles, Noélia

N1 - Funding Information: This work was partially funded by MIUR Italian grant PRIN 2009 on Finitary and non-Finitary Probabilistic Methods in Economics within the project The Growth of Firms and Countries: Distributional Properties and Economic Determinants.

PY - 2012/6

Y1 - 2012/6

N2 - The relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a stochastic process.

AB - The relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a stochastic process.

KW - Compound renewal process

KW - Continuous time random walk

KW - Fractional Poisson process

KW - Inverse stable subordinator

KW - MWright functions

KW - Mittag-Leffler waiting time

KW - Quadratic variation

UR - https://www.scopus.com/pages/publications/84867453750

U2 - 10.2478/s13540-012-0023-2

DO - 10.2478/s13540-012-0023-2

M3 - Article

SN - 1311-0454

VL - 15

SP - 314

EP - 331

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 2

ER -

On the convergence of quadratic variation for compound fractional poisson processes

Abstract

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