Open AccessBook
Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
TLDR
In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.Abstract:
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.read more
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