Kallenberg O. Foundations of Modern Probability

3rd ed. — Springer, 2021. — 930 p. — (Probability Theory and Stochastic Modelling 99). — ISBN 3030618706.Many years have passed since I started writing the first edition, and the need for a comprehensive coverage of modern probability has become more urgent than ever. I am grateful for the opportunity to publish a new, thoroughly revised and expanded edition. Much new material has been added, and there are even entirely new chapters on subjects like Malliavin calculus, multivariate arrays, and stochastic differential geometry (with so much else still missing). To facilitate the reader’s access and overview, I have grouped the material together into ten major areas, each arguably indispensable to any serious student and researcher, regardless of area of specialization.
To me, every great mathematical theorem should be a revelation, prompting us to exclaim: “Wow, this is just amazing, how could it be true ?” I have spent countless hours, trying to phrase every result in its most striking form, in my efforts to convey to the reader my own excitement. My greatest hope is that the reader will share my love for the subject, and help me to keep it alive.Preface to the First Edition.
Preface to the Second Edition.
Preface to the Third Edition.Words of Wisdom and Folly.
Introduction and Reading Guide.
Measure Theoretic Prerequisites.
Some Classical Probability Theory.
Conditioning and Martingales.
Markovian and Related Structures.
Some Fundamental Processes.
Stochastic Calculus and Applications.
Convergence and Approximation.
Stationarity, Symmetry and Invariance.
Random Sets and Measures.
SDEs, Diffusions, and Potential Theory.
Appendices.
Notes and References.Indices.True PDF