Probability theory / Heinz Bauer ; translated from the German by Robert B. Burckel
- Author
- Bauer, Heinz, 1928-
- Uniform Title
- Wahrscheinlichkeitstheorie. English
- Published
- Berlin ; New York : Walter de Gruyter, 1996.
- Physical Description
- 1 online resource (xv, 523 pages) : illustrations
- Additional Creators
- Burckel, R. B., 1939-
Access Online
- Series
- Language Note
- English.
- Contents
- 23 Uniqueness and Continuity Theorems24 Normal distribution and independence; 25 Differentiability of Fourier transforms; 26 Continuous mappings into the circle; Chapter VI Limit Distributions; 27 Examples of limit theorems; 28 The Central Limit Theorem; 29 Infinitely divisible distributions; 30 Gauss measures and multi-dimensional central limit theorem; Chapter VII Law of the Iterated Logarithm; 31 Posing the question and elementary preparations; 32 Probabilistic preparations; 33 Strassen's theorem of the iterated logarithm; 34 Supplements., 49 Optional times and optional sampling50 The strong Markov property; 51 Prospectus; Bibliography; Symbol Index; Name Index; General Index., 9 Infinite products of probability spacesChapter III Laws of Large Numbers; 10 Posing the question; 11 Zero-one laws; 12 Strong Law of Large Numbers; 13 Applications; 14 Almost sure convergence of infinite series; Chapter IV Martingales; 15 Conditional expectations; 16 Martingales -- definition and examples; 17 Transformation via optional times; 18 Inequalities for supermartingales; 19 Convergence theorems; 20 Applications; Chapter V Fourier Analysis; 21 Integration of complex-valued functions; 22 Fourier transformation and characteristic functions., Chapter VIII Construction of Stochastic Processes35 Projective limits of probability measures; 36 Kernels and semigroups of kernels; 37 Processes with stationary and independent increments; 38 Processes with pre-assigned path-set; 39 Continuous modifications; 40 Brownian motion as a stochastic process; 41 Poisson processes; 42 Markov processes; 43 Gauss processes; 44 Conditional distributions; Chapter IX Brownian Motion; 45 Brownian motion with filtration and martingales; 46 Maximal inequalities for martingales; 47 Behavior of Brownian paths; 48 Examples of stochastic integrals., and Preface; Table of Contents; Interdependence of chapters; Notation; Introduction; Chapter I Basic Concepts of the Theory; 1 Probability spaces and the language of probability theory; 2 Laplace experiments and conditional probabilities; 3 Random variables: Distribution, expected value, variance, Jensen's inequality; 4 Special distributions and their properties; 5 Convergence of random variables and distributions; Chapter II Independence; 6 Independent events and σ-algebras; 7 Independent random variables; 8 Products and sums of independent random variables
- Subject(s)
- ISBN
- 9783110814668 (electronic bk.)
3110814668 (electronic bk.)
3110139359 (alk. paper)
9783110139358 - Digital File Characteristics
- data file
- Bibliography Note
- Includes bibliographical references (pages 493-500) and indexes.
View MARC record | catkey: 43615193