Stable sub-Gaussian models constructed by Poisson processes

Dai Hongshuai; Li Yuqiang

doi:10.1016/S0252-9602(11)60373-1

Stable sub-Gaussian models constructed by Poisson processes

Dai Hongshuai
, Li Yuqiang^*

^*Corresponding author for this work

School of Statistics

Central South University
Guangxi University

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

2 Scopus citations

Abstract

In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.

Original language	English
Pages (from-to)	1945-1958
Number of pages	14
Journal	Acta Mathematica Scientia
Volume	31
Issue number	5
DOIs	https://doi.org/10.1016/S0252-9602(11)60373-1
State	Published - Sep 2011

Keywords

Poisson process
Riemann integral
Stable sub-Gaussian process
Weak convergence

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10.1016/S0252-9602(11)60373-1

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title = "Stable sub-Gaussian models constructed by Poisson processes",

abstract = "In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.",

keywords = "Poisson process, Riemann integral, Stable sub-Gaussian process, Weak convergence",

author = "Dai Hongshuai and Li Yuqiang",

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AU - Hongshuai, Dai

AU - Yuqiang, Li

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N2 - In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.

AB - In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.

KW - Poisson process

KW - Riemann integral

KW - Stable sub-Gaussian process

KW - Weak convergence

UR - https://www.scopus.com/pages/publications/79961178767

U2 - 10.1016/S0252-9602(11)60373-1

DO - 10.1016/S0252-9602(11)60373-1

M3 - 文章

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SN - 0252-9602

VL - 31

SP - 1945

EP - 1958

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 5

ER -

Stable sub-Gaussian models constructed by Poisson processes

Abstract

Keywords

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