On the characteristics of a class of Gaussian processes within the white noise space setting

Daniel Alpay; Haim Attia; David Levanony

doi:10.1016/j.spa.2010.03.004

On the characteristics of a class of Gaussian processes within the white noise space setting

Daniel Alpay, Haim Attia, David Levanony

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

19 Scopus citations

Abstract

Using the white noise space framework, we construct and study a class of Gaussian processes with stationary increments, which include as particular cases the Brownian and fractional Brownian motions. The derivative processes are computed using Hida's theory of stochastic distributions.

Original language	English
Pages (from-to)	1074-1104
Number of pages	31
Journal	Stochastic Processes and their Applications
Volume	120
Issue number	7
DOIs	https://doi.org/10.1016/j.spa.2010.03.004
State	Published - 1 Jul 2010

Keywords

Fractional Brownian motion
White noise space
Wick product

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/j.spa.2010.03.004

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title = "On the characteristics of a class of Gaussian processes within the white noise space setting",

abstract = "Using the white noise space framework, we construct and study a class of Gaussian processes with stationary increments, which include as particular cases the Brownian and fractional Brownian motions. The derivative processes are computed using Hida's theory of stochastic distributions.",

keywords = "Fractional Brownian motion, White noise space, Wick product",

author = "Daniel Alpay and Haim Attia and David Levanony",

note = "Funding Information: D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. The research of the authors was supported in part by the Israel Science Foundation grant 1023/07 .",

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AU - Alpay, Daniel

AU - Attia, Haim

AU - Levanony, David

N1 - Funding Information: D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. The research of the authors was supported in part by the Israel Science Foundation grant 1023/07 .

PY - 2010/7/1

Y1 - 2010/7/1

N2 - Using the white noise space framework, we construct and study a class of Gaussian processes with stationary increments, which include as particular cases the Brownian and fractional Brownian motions. The derivative processes are computed using Hida's theory of stochastic distributions.

AB - Using the white noise space framework, we construct and study a class of Gaussian processes with stationary increments, which include as particular cases the Brownian and fractional Brownian motions. The derivative processes are computed using Hida's theory of stochastic distributions.

KW - Fractional Brownian motion

KW - White noise space

KW - Wick product

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DO - 10.1016/j.spa.2010.03.004

M3 - Article

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SN - 0304-4149

VL - 120

SP - 1074

EP - 1104

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 7

ER -

On the characteristics of a class of Gaussian processes within the white noise space setting

Abstract

Keywords

ASJC Scopus subject areas

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