Foundations of Modern Probability

Cover
Springer Science & Business Media, 08.01.2002 - 638 Seiten
0 Rezensionen

About the first edition:

To sum it up, one can perhaps see a distinction among advanced probability books into those which are original and path-breaking in content, such as Levy's and Doob's well-known examples, and those which aim primarily to assimilate known material, such as Loeve's and more recently Rogers and Williams'. Seen in this light, Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands.

- Mathematical Reviews

This new edition contains four new chapters as well as numerous improvements throughout the text. There are new chapters on measure Theory-key results, ergodic properties of Markov processes and large deviations.

 

Was andere dazu sagen - Rezension schreiben

Es wurden keine Rezensionen gefunden.

Inhalt

Measure Theory Basic Notions
1
Measure Theory Key Results
23
Processes Distributions and Independence
45
Random Sequences Series and Averages
62
Characteristic Functions and Classical Limit Theorems
83
Conditioning and Disintegration
103
Martingales and Optional Times
119
Markov Processes and DiscreteTime Chains
140
Feller Processes and Semigroups
367
Ergodic Properties of Markov Processes
390
Stochastic Differential Equations and Martingale Problems
412
Local Time Excursions and Additive Functionals
428
OneDimensional SDEs and Diffusions
450
Connections with PDEs and Potential Theory
470
Predictability Compensation and Excessive Functions
490
Semimartingales and General Stochastic Integration
515

Random Walks and Renewal Theory
159
Stationary Processes and Ergodic Theory
178
Special Notions of Symmetry and Invariance
202
Poisson and Pure JumpType Markov Processes
224
Gaussian Processes and Brownian Motion
249
Skorohod Embedding and Invariance Principles
270
Independent Increments and Infinite Divisibility
285
Convergence of Random Processes Measures and Sets
307
Stochastic Integrals and Quadratic Variation
329
Continuous Martingales and Brownian Motion
350
Large Deviations
537
Appendices
561
A2 Some Special Spaces
562
Historical and Bibliographical Notes
569
Bibliography
596
Symbol Index
621
Author Index
623
Subject Index
629
Urheberrecht

Andere Ausgaben - Alle anzeigen

Häufige Begriffe und Wortgruppen

Verweise auf dieses Buch

Alle Ergebnisse von Google Books »

Über den Autor (2002)

Olav Kallenberg received his Ph.D. in 1972 from Chalmers University in Gothenburg, Sweden. After teaching for many years at Swedish universities, he moved in 1985 to the US, where he is currently Professor of Mathematics at Auburn University. He is well known for his previous books Random Measures (4th edition, 1986) and Foundations of Modern Probability (2nd edition, 2002) 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 1991a "94, he served as the Editor in Chief of Probability Theory and Related Fields. Professor Kallenberg is an elected fellow of the Institute of Mathematical Statistics.

Bibliografische Informationen