Theory of Probability and Mathematical Statistics
Regularity properties of random wavelet series
Céline Esser, Stéphane Jaffard and Béatrice Vedel
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Abstract: We study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens for Fourier series, the randomization of almost every continuous function gives an almost surely nowhere locally bounded function.
Keywords: Random wavelet series, random Fourier series, unconditional bases, generic regularity
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