Probability theory
(eBook)
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Author:
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Series:
De Gruyter studies in mathematics ; volume 23.
Published:
Berlin ; New York : Walter de Gruyter, 1996.
Format:
eBook
ISBN:
9783110814668, 3110814668
Physical Desc:
1 online resource (xv, 523 pages) : illustrations
Status:
Ebsco (CCU)
Description
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
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Citations
APA Citation (style guide)
Bauer, H., & Burckel, R. B. (1996). Probability theory. Berlin ; New York, Walter de Gruyter.
Chicago / Turabian - Author Date Citation (style guide)Bauer, Heinz, 1928- and Robert B. Burckel. 1996. Probability Theory. Berlin ; New York, Walter de Gruyter.
Chicago / Turabian - Humanities Citation (style guide)Bauer, Heinz, 1928- and Robert B. Burckel, Probability Theory. Berlin ; New York, Walter de Gruyter, 1996.
MLA Citation (style guide)Bauer, Heinz and Robert B Burckel. Probability Theory. Berlin ; New York, Walter de Gruyter, 1996.
Note! Citation formats are based on standards as of July 2022. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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Language:
English
UPC:
10.1515/9783110814668
Notes
Bibliography
Includes bibliographical references (pages 493-500) and indexes.
Language
English.
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Grouped Work ID:
c414c11f-003b-5ad3-b96b-cb103a81eaa9
Record Information
Last File Modification Time | Apr 05, 2024 09:31:37 PM |
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Last Grouped Work Modification Time | Apr 05, 2024 09:12:39 PM |
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240 | 1 | 0 | |a Wahrscheinlichkeitstheorie.|l English |
245 | 1 | 0 | |a Probability theory /|c Heinz Bauer ; translated from the German by Robert B. Burckel. |
260 | |a Berlin ;|a New York :|b Walter de Gruyter,|c 1996. | ||
300 | |a 1 online resource (xv, 523 pages) :|b illustrations | ||
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490 | 1 | |a De Gruyter studies in mathematics ;|v 23 | |
504 | |a Includes bibliographical references (pages 493-500) and indexes. | ||
505 | 0 | |a 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. | |
505 | 0 | |a 49 Optional times and optional sampling50 The strong Markov property; 51 Prospectus; Bibliography; Symbol Index; Name Index; General Index. | |
505 | 0 | |a 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. | |
505 | 0 | |a 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. | |
546 | |a English. | ||
650 | 0 | |a Probabilities. | |
650 | 6 | |a Probabilités. | |
650 | 7 | |a probability.|2 aat | |
650 | 7 | |a MATHEMATICS|x Probability & Statistics|x General.|2 bisacsh | |
650 | 7 | |a Probabilities|2 fast | |
700 | 1 | |a Burckel, Robert B. | |
776 | 0 | 8 | |i Print version:|a Bauer, Heinz, 1928-|s Wahrscheinlichkeitstheorie. English.|t Probability theory.|d Berlin ; New York : Walter de Gruyter, 1996|w (DLC) 95039173 |
830 | 0 | |a De Gruyter studies in mathematics ;|v 23. | |
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880 | 0 | |6 505-00/(S|a 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 | |
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