Limit theorems for Hilbert space-valued linear processes under long range dependence

Dueker MC (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Stochastic Processes and their Applications Elsevier

Book Volume: 128

Pages Range: 1439-1465

Journal Issue: 5

DOI: 10.1016/j.spa.2017.07.015

Abstract

Let (Xk)k∈Z be a linear process with values in a separable Hilbert space H given by Xk=∑j=0 ^∞(j+1)^−Nεk−j for each k∈Z, where N:H→H is a bounded, linear normal operator and (εk)k∈Z is a sequence of independent, identically distributed H-valued random variables with Eε0=0 and E‖ε0‖²<∞. We investigate the central and the functional central limit theorem for (Xk)k∈Z when the series of operator norms ∑j=0 ^∞‖(j+1)^−N‖op diverges. Furthermore, we show that the limit process in case of the functional central limit theorem generates an operator self-similar process.

Involved external institutions

Ruhr-Universität Bochum (RUB)

Germany (DE)

How to cite

APA:

Dueker, M.-C. (2018). Limit theorems for Hilbert space-valued linear processes under long range dependence. Stochastic Processes and their Applications, 128(5), 1439-1465. https://dx.doi.org/10.1016/j.spa.2017.07.015

MLA:

Dueker, Marie-Christine. "Limit theorems for Hilbert space-valued linear processes under long range dependence." Stochastic Processes and their Applications 128.5 (2018): 1439-1465.

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