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Letbe the linear processes, whereis an absolutely summable sequence of real numbers andis a sequence of real stationary independent random variables under the sub-linear expectation spaceIn 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.

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