Foundations of Modern Probability

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Springer Science & Business Media, 2006. 5. 10. - 523페이지
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From the reviews of 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 "... 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." 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. ..." Metrica This new edition contains four new chapters as well as numerous improvements throughout the text.
 

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Elements of Measure Theory
1
Processes Distributions and Independence
22
Random Sequences Series and Averages
39
Characteristic Functions and Classical Limit Theorems
60
Conditioning and Disintegration
80
Martingales and Optional Times
96
Markov Processes and DiscreteTime Chains
117
Random Walks and Renewal Theory
136
Stochastic Integrals and Quadratic Variation
275
Continuous Martingales and Brownian Motion
296
Feller Processes and Semigroups
313
Stochastic Differential Equations and Martingale Problems
335
Local Time Excursions and Additive Functionals
350
OneDimensional SDEs and Diffusions
371
PDEConnections and Potential Theory
390
Predictability Compensation and Excessive Functions
409

Stationary Processes and Ergodic Theory
156
Poisson and Pure JumpType Markov Processes
176
Gaussian Processes and Brownian Motion
199
Skorohod Embedding and Invariance Principles
220
Independent Increments and Infinite Divisibility
234
Convergence of Random Processes Measures and Sets
255
Semimartingales and General Stochastic Integration
433
Appendices
455
Historical and Bibliographical Notes
464
Bibliography
486
Indices
509
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저자 정보 (2006)

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.

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