Let {Y_i,−∞ < i < ∞} be a doubly infinite sequence of identically distributed ρ-mixing random variables, {a_i,−∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of the moving average processes {Σ_{i=-∞}^∞aiY_{i+n}, n ≥ 1}.
Limiting behaviour of moving average processes under rho-mixing assumption
GIULIANO, RITA;
2010-01-01
Abstract
Let {Y_i,−∞ < i < ∞} be a doubly infinite sequence of identically distributed ρ-mixing random variables, {a_i,−∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of the moving average processes {Σ_{i=-∞}^∞aiY_{i+n}, n ≥ 1}.File in questo prodotto:
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