Foundations of Modern ProbabilitySpringer Science & Business Media, 2006. 5. 10. - 523페이지 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. |
목차
| 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 |
| 486 | |
| 509 | |
자주 나오는 단어 및 구문
arbitrary assume basic bounded Brownian motion Chapter choose compact condition continuous local martingale Corollary countable decomposition define denote dominated convergence Doob eacists equation equivalent ergodic exists extends Feller process filtration Fubini's theorem function f Gaussian Hence Hint independent inequality inf{t initial distribution introduce invariant large numbers Lemma Lévy processes lim sup locally finite mapping Markov chain Markov process Markov property martingale measurable function measurable space metric space monotone class argument O-field obtain optional particular point process Poisson process predictable probability measure Proof of Theorem Proposition prove random elements random measure random variables random walk recurrent right-continuous semigroup semimartingale sequence stochastic integral strong Markov property submartingale symmetric theory time-change uniqueness write