Continuous Martingales and Brownian Motion (Grundlehren der mathematischen Wissenschaften 293 Softcover reprint of hardcover 3rd ed. 1999)

Continuous Martingales and Brownian Motion (Grundlehren der mathematischen Wissenschaften 293 Softcover reprint of hardcover 3rd ed. 1999)

By: Marc Yor (author), Daniel Revuz (author)Paperback

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Description

"This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises." -BULLETIN OF THE L.M.S.

Contents

0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.- VIII. Girsanov's Theorem and First Applications.- IX. Stochastic Differential Equations.- X. Additive Functionals of Brownian Motion.- XI. Bessel Processes and Ray-Knight Theorems.- XII. Excursions.- XIII. Limit Theorems in Distribution.- 1. Gronwall's Lemma.- 2. Distributions.- 3. Convex Functions.- 4. Hausdorff Measures and Dimension.- 5. Ergodic Theory.- 6. Probabilities on Function Spaces.- 7. Bessel Functions.- 8. Sturm-Liouville Equation.- Index of Notation.- Index of Terms.- Catalogue.

Product Details

  • ISBN13: 9783642084003
  • Format: Paperback
  • Number Of Pages: 602
  • ID: 9783642084003
  • weight: 943
  • ISBN10: 3642084001
  • edition: Softcover reprint of hardcover 3rd ed. 1999

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