A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations

In this paper, we derive a self-normalized functional limit theorem for strictly stationary linear processes with i.i.d. heavy-tailed innovations and random coefficients under the condition that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series. T...

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Bibliographic Details
Published in:Lithuanian mathematical journal 2023-07, Vol.63 (3), p.305-336
Main Author: Krizmanić, Danijel
Format: Article
Language:English
Subjects:
Actuarial Sciences
Coefficients
Innovations
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability Theory and Stochastic Processes
Theorems
Topology
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Summary:In this paper, we derive a self-normalized functional limit theorem for strictly stationary linear processes with i.i.d. heavy-tailed innovations and random coefficients under the condition that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series. The convergence takes place in the space of càdlàg functions on [0 , 1] with the Skorokhod M 2 topology.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-023-09601-3