Large deviation principle for linear processes generated by real stationary sequences under the sub-linear expectation

Wei Liu and Yong Zhang

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 16, 5727-5741

Abstract: Let {Xk=∑j=−∞+∞ajξk−j, k≥1} be the linear processes, where {aj, j∈Z} is an absolutely summable sequence of real numbers and ∑j=−∞+∞aj≠0, {ξj,j∈Z} is a sequence of real stationary independent random variables under the sub-linear expectation space (Ω,H,E). In the framework of sub-linear expectation space, the Beveridge–Nelson decomposition of linear processes and the sub-additivity of capacity are used to establish the large deviation principle for linear processes in the sense of upper probability.

Date: 2023
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DOI: 10.1080/03610926.2021.2018462

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