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＜電子ブック＞
Foundations of Modern Probability / by Olav Kallenberg
(Probability and Its Applications)

版	2nd ed. 2002.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2002
本文言語	英語
大きさ	XX, 638 p : online resource
冊子体	Foundations of modern probability / Olav Kallenberg
著者標目	*Kallenberg, Olav author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Topology FREE:Probability Theory FREE:Topology
一般注記	Measure Theory-Basic Notions * Measure Theory-Key Results -- 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 -- Special Notions of Symmetry and Invariance -- 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 -- Ergodic Properties of Markov Processes -- Stochastic Differential Equations and Martingale Problems -- Local Time, Excursions, and Additive Functionals -- One-Dimensional SDEs and Diffusions -- Connections with PDEs and Potential Theory -- Predictability, Compensation, and Excessive Functions -- Semimartingales and General Stochastic Integration -- Large Deviations -- Appendix 1: Advanced From the reviews of the first editions: "... 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." F.B. Knight, Mathematical Reviews "...Indeed the monograph has the potential to become a (possibly even "the") major reference book on large parts of probability theory for the next decade or more." M. Scheutzow, Zentralblatt "The theory of probability has grown exponentially during the second half of the twentieth century and the idea of writing a single volume that could serve as a general reference for much of the modern theory seems almost foolhardy. Yet this is precisely what Professor Kallenberg has attempted in the volume under review and he has accomplished it brilliantly...It is astonishing that a single volume of just over five hundred pages could contain so much material presented with complete rigor and still be at least formally self-contained..." R.K. Getoor, Metrika This new edition contains four new chapters as well as numerous improvements throughout the text. 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." Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4757-4015-8

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