Some Random Series of Functions [Paperback]

The subject matter of Some Random Series of Functions is important and has wide application in mathematics, statistics, engineering, and physics.This second edition covers random series in Banach and Hilbert spaces, random Taylor or Fourier series, Brownian motion and other Gaussian processes, plus certain types of random sets and measures--subjects of application in mathematics, statistics, engineering and physics.This second edition covers random series in Banach and Hilbert spaces, random Taylor or Fourier series, Brownian motion and other Gaussian processes, plus certain types of random sets and measures--subjects of application in mathematics, statistics, engineering and physics.The second edition of Some Random Series of Functions, covers random series in Banach and Hilbert spaces, random Taylor or Fourier series, Brownian motion and other Gaussian processes, plus certain types of random sets and measures. The subject matter of this book is important and has wide application in mathematics, statistics, engineering, and physics. Professor Kahane's presentation is suitable even for beginning graduate students in probability and analysis (exercises are provided throughout), as well as nonspecialists in the other disciplines to which this subject has application.1. A few tools from probability theory; 2. Random series in a Banach space; 3. Random series in a Hilbert space; 4. Random Taylor series; 5. Random Fourier series; 6. A bound for random trigonometric polynomials; 7. Conditions on coefficients for regularity; 8. Conditions on coefficients for irregularity; 9. Random point masses on the circle; 10. A few geometric notions; 11. Random translates and coverings; 12. Gaussian variables and Gaussian series; 13. Gaussian Taylor series; 14. Gaussian Fourier series; 15. Boundedness and continuity for Gaussian processes; 16. The Brownian motion; 17. Brownian images in harmonic analysis; 18. Fractional Brownian images and level sets. ...a rewarding [book], certain to l3.