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Limit Theorems for Functionals of Random Walks
A. N. Borodin and I. A. Ibragimov
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Proceedings of the Steklov Institute of Mathematics
1995; 259 pp; softcover
Volume: 195
ISBN-10: 0-8218-0438-3
ISBN-13: 978-0-8218-0438-4
List Price: US$269
Member Price: US$215.20
Order Code: STEKLO/195
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This book examines traditional problems in the theory of random walks: limit theorems for additive and multiadditive functionals defined on a random walk. Although the problems are traditional, the methods presented here are new. One of the methods involves expressing the functionals in terms of a suitable integral transform (such as the Fourier transform), and another method is based on results on convergence of processes generated by random walks to Brownian local time. These methods can be used to prove the convergence of functionals of random walks under very general assumptions about the functional and for a very broad class of random walks. The book is intended for experts in probability theory and its applications, as well as for undergraduate and graduate students specializing in these areas.

Readership

Research mathematicians.

Table of Contents

  • Preliminary facts
  • Distributions of functionals of Brownian local time
  • Limit theorems for functionals of normalized sums
  • Limit theorems for additive and multiadditive functionals of a random walk
  • Invariance principle for local times
  • Bibliographical comments
  • Bibliography
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