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Stochastic Analysis and Related TopicsDecomposition and Limit Theorems for a Class of Self-Similar Gaussian Processes

Stochastic Analysis and Related Topics: Decomposition and Limit Theorems for a Class of... [We introduce a new class of self-similar Gaussian stochastic processes, where the covariance is defined in terms of a fractional Brownian motion and another Gaussian process. A special case is the solution in time to the fractional-colored stochastic heat equation described in Tudor (Analysis of variations for self-similar processes: a stochastic calculus approach. Springer, Berlin, 2013). We prove that the process can be decomposed into a fractional Brownian motion (with a different parameter than the one that defines the covariance), and a Gaussian process first described in Lei and Nualart (Stat Probab Lett 79:619–624, 2009). The component processes can be expressed as stochastic integrals with respect to the Brownian sheet. We then prove a central limit theorem about the Hermite variations of the process.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Stochastic Analysis and Related TopicsDecomposition and Limit Theorems for a Class of Self-Similar Gaussian Processes

Part of the Progress in Probability Book Series (volume 72)
Editors: Baudoin, Fabrice; Peterson, Jonathon
Harnett, Daniel; Nualart, David
Stochastic Analysis and Related Topics — Sep 27, 2017
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17 pages

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References (16)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG 2017
ISBN
978-3-319-59670-9
Pages
99 –116
DOI
10.1007/978-3-319-59671-6_5
Publisher site
See Chapter on Publisher Site

Abstract

[We introduce a new class of self-similar Gaussian stochastic processes, where the covariance is defined in terms of a fractional Brownian motion and another Gaussian process. A special case is the solution in time to the fractional-colored stochastic heat equation described in Tudor (Analysis of variations for self-similar processes: a stochastic calculus approach. Springer, Berlin, 2013). We prove that the process can be decomposed into a fractional Brownian motion (with a different parameter than the one that defines the covariance), and a Gaussian process first described in Lei and Nualart (Stat Probab Lett 79:619–624, 2009). The component processes can be expressed as stochastic integrals with respect to the Brownian sheet. We then prove a central limit theorem about the Hermite variations of the process.]

Published: Sep 27, 2017

Keywords: Fractional Brownian motion; Hermite variations; Self-similar processes; Stochastic heat equation; 60F05; 60G18; 60H07

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