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- W2016323189 abstract "We introduce a broad class of self-similar processes ${Z(t),tge 0}$ called generalized Hermite process. They have stationary increments, are defined on a Wiener chaos with Hurst index $Hin (1/2,1)$, and include Hermite processes as a special case. They are defined through a homogeneous kernel $g$, called 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 $Z^beta(t)$ of $Z(t)$, which allows $Hin (0,1/2)$. Corresponding non-central limit theorems are established. We also give a multivariate limit theorem which mixes central and non-central limit theorems." @default.
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- W2016323189 date "2014-04-01" @default.
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- W2016323189 title "Generalized Hermite processes, discrete chaos and limit theorems" @default.
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- W2016323189 doi "https://doi.org/10.1016/j.spa.2013.12.011" @default.
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