Foundations of Modern Probability

Olav Kallenberg

646 pages, parution le 01/02/2002 (2^eme édition)

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Résumé

This book is unique for its broad and yet comprehensive coverage of modern probability theory, ranging from first principles and standard textbook material to more advanced topics. In spite of the economical exposition, careful proofs are provided for all main results. Though primarily intended as a general reference for researchers and graduate students in probability theory and related areas of analysis, the book is also suitable as a text for graduate and seminar courses on all levels, from elementary to advanced. Numerous easy to more challenging exercises are provided, especially for the early chapters.

This new edition contains four new chapters as well as numerous improvements throughout the text.

Contents

Elements of Measure Theory
Processes, Distributions, and Independence
Random Sequences, Series, and Averages
Characteristic Functions and Classical Limit Theorems
Conditioning and Disintegration
Martingales and Optional Times
Markov Processes and Discrete-Time Chains
Random Walks and Renewal Theory
Stationary Processes and Ergodic Theory
Poisson and Pure Jump-Type Markov Processes
Gaussian Processes and Brownian Motion
Skorohod Embedding and Invariance Principles
Independent Increments and Infinite Divisibility
Convergence of Random Processes, Measures, and Sets
Stochastic Integrals and Quadratic Variation
Continuous Martingales and Brownian Motion
Feller Processes and Semigroups
Stochastic Differential Equations and Martingale Problems
Local Time, Excursions, and Additive Functionals
One-Dimensional SDEs and Diffusions
PDE-Connections and Potential Theory
Predictability, Compensation, and Excessive Functions
Semimartingales and General Stochastic Integration

Appendices
Historical and Bibliographical Notes
Bibliography
Indices

L'auteur - Olav Kallenberg

Olav Kallenberg was educated in Sweden, where he received his Ph.D. in 1972 from Chalmers University. After teaching for many years at Swedish universities, he moved in 1985 to the U.S., where he is currently a Professor of Mathematics at Auburn University. He is known for his book "Random Measures" (4th edition, 1986) and for numerous research papers in all areas of probability. In 1977, he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. In 1991-94, he served as the Editor-in-Chief of "Probability Theory and Related Fields."

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Olav Kallenberg
Parution	01/02/2002
Édition	2^eme édition
Nb. de pages	646
Format	16 x 24
Couverture	Relié
Poids	1060g
Intérieur	Noir et Blanc
EAN13	9780387953137
ISBN13	978-0-387-95313-7