Markov processes, Gaussian processes, and local times

著者

書誌事項

Markov processes, Gaussian processes, and local times

Michael B. Marcus, Jay Rosen

（Cambridge studies in advanced mathematics, 100）

Cambridge University Press, 2011

  • : pbk

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注記

"First paperback edition (with corrections) 2011"--T.p. verso

Includes bibliographical references (p. 603-610) and indexes

内容説明・目次

内容説明

This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum and then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.

目次

  • 1. Introduction
  • 2. Brownian motion and Ray-Knight theorems
  • 3. Markov processes and local times
  • 4. Constructing Markov processes
  • 5. Basic properties of Gaussian processes
  • 6. Continuity and boundedness
  • 7. Moduli of continuity
  • 8. Isomorphism theorems
  • 9. Sample path properties of local times
  • 10. p-Variation
  • 11. Most visited site
  • 12. Local times of diffusions
  • 13. Associated Gaussian processes
  • Appendices: A. Kolmogorov's theorem for path continuity
  • B. Bessel processes
  • C. Analytic sets and the projection theorem
  • D. Hille-Yosida theorem
  • E. Stone-Weierstrass theorems
  • F. Independent random variables
  • G. Regularly varying functions
  • H. Some useful inequalities
  • I. Some linear algebra
  • References
  • Index.

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