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This is a substantially revised and updated edition of Professor Kahane's celebrated book Some Random Series of Functions, first published in 1968. It covers random series in Banach or Hilbert spaces, random Taylor or Fourier series, Brownian motion-and other Gaussian processes, and certain types of random set and measures. In the new chapters Professor Kahane discusses geometric notions related to Hausdorff measures and dimensions, sets obtained by removing random convex bodies from a given body, images and level sets of a fractional Brownian motion and adds extra material on Brownian motion in general. He also considers continuity properties of sample functions of Gaussian processes and their application to random Fourier series (related to work by Dudley, Fernique, Marcus and Pisier). Some of this material has not been published before.

Mathematical analysis --- Probability theory --- 519.219 --- Functions --- Random variables --- Series --- Stochastic processes --- Random processes --- Probabilities --- Algebra --- Mathematics --- Processes, Infinite --- Sequences (Mathematics) --- Chance variables --- Stochastic variables --- Variables (Mathematics) --- Analysis (Mathematics) --- Differential equations --- Numbers, Complex --- Set theory --- Calculus --- Random functions of several variables --- Functions. --- Random variables. --- Series. --- Stochastic processes. --- 519.219 Random functions of several variables --- Fonctions (mathématiques) --- Séries (mathématiques) --- Variables aléatoires. --- Processus stochastiques. --- Fonctions (mathématiques) --- Séries (mathématiques) --- Variables aléatoires.

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Fourier series --- Stochastic processes

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Fourier series. --- Banach algebras. --- Functions, Continuous.

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Harmonic analysis. Fourier analysis