On random Fourier series
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- by Jack Cuzick and Tze Leung Lai PDF
- Trans. Amer. Math. Soc. 261 (1980), 53-80 Request permission
Abstract:
Motivated by Riemann’s ${R_1}$ summation method for i.i.d. random variables ${X_1}, {X_2}, \ldots$, this paper studies random Fourier series of the form $\sum \nolimits _1^\infty {{a_n}{X_n} \sin (nt + {\Phi _n})}$, where $\{ {a_n}\}$ is a sequence of constants and $\{ {\Phi _n}\}$ is a sequence of independent random variables which are independent of $\{ {X_n}\}$. Questions of continuity and of unboundedness are analyzed through the interplay between the asymptotic properties of $\{ {a_n}\}$ and the tail distribution of ${X_1}$. A law of the iterated logarithm for the local behavior of the series is also obtained and extends the classical result for Brownian motion to a general class of random Fourier series.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 261 (1980), 53-80
- MSC: Primary 60G17; Secondary 42A20, 60F15
- DOI: https://doi.org/10.1090/S0002-9947-1980-0576863-8
- MathSciNet review: 576863