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

Research output: Contribution to journal › Article › 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.

Original language	English
Pages (from-to)	314-331
Number of pages	18
Journal	Fractional Calculus and Applied Analysis
Volume	15
Issue number	2
DOIs	https://doi.org/10.2478/s13540-012-0023-2
Publication status	Published - Jun 2012
Externally published	Yes

Keywords

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

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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.",

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AU - Viles, Noélia

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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.

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KW - Compound renewal process

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KW - Inverse stable subordinator

KW - MWright functions

KW - Mittag-Leffler waiting time

KW - Quadratic variation

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JO - Fractional Calculus and Applied Analysis

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On the convergence of quadratic variation for compound fractional poisson processes

Abstract

Keywords

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