Generalized Hermite processes, discrete chaos and limit theorems

Shuyang Bai and Murad S. Taqqu

Stochastic Processes and their Applications, 2014, vol. 124, issue 4, 1710-1739

Abstract: We introduce a broad class of self-similar processes {Z(t),t≥0} called generalized Hermite processes. They have stationary increments, are defined on a Wiener chaos with Hurst index H∈(1/2,1), and include Hermite processes as a special case. They are defined through a homogeneous kernel g, called the “generalized Hermite kernel”, which replaces the product of power functions in the definition of Hermite processes. The generalized Hermite kernels g can also be used to generate long-range dependent stationary sequences forming a discrete chaos process {X(n)}. In addition, we consider a fractionally-filtered version Zβ(t) of Z(t), which allows H∈(0,1/2). Corresponding non-central limit theorems are established. We also give a multivariate limit theorem which mixes central and non-central limit theorems.

Keywords: Long memory; Discrete chaos; Wiener chaos; Limit theorem (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (11)

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DOI: 10.1016/j.spa.2013.12.011

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