A User's Guide to Measure Theoretic Probability

David D. Pollard

352 pages, parution le 15/02/2002

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Résumé

Rigorous probabilistic arguments, built on the foundation of measure theory introduced seventy years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.

Contents

Preface

1. Motivation
2. A modicum of measure theory
3. Densities and derivatives
4. Product spaces and independence
5. Conditioning
6. Martingale et al
7. Convergence in distribution
8. Fourier transforms
9. Brownian motion
10. Representations and couplings
11. Exponential tails and the law of the iterated logarithm
12. Multivariate normal distributions

Appendix A. Measures and integrals
Appendix B. Hilbert spaces
Appendix C. Convexity
Appendix D. Binomial and normal distributions
Appendix E. Martingales in continuous time
Appendix F. Generalized sequences.

Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	David D. Pollard
Parution	15/02/2002
Nb. de pages	352
Format	17,6 x 25,4
Couverture	Broché
Poids	650g
Intérieur	Noir et Blanc
EAN13	9780521002899
ISBN13	978-0-521-00289-9