Lacunary systems and generalized linear processes

Tze Leung Lai and Ching Zong Wei

Stochastic Processes and their Applications, 1983, vol. 14, issue 2, 187-199

Abstract: Herein we obtain several almost sure and Lp convergence properties of generalized linear processes. When the generalized linear process is generated by an orthonormal Sp system (which includes the classical i.i.d. white noise, Lp bounded martingale difference sequences and weakly multiplicative sequences as special cases), it is shown that these convergence properties are related to certain second order properties of the process.

Date: 1983
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