Measure theory and probability theory
This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended prima...
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| Auteurs principaux: | , , |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2006. |
| Collection: | Springer Texts in Statistics
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| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Description d'après consultation du 11 avril 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Measure theory and probability theory, Krishna B. Athreya, Soumendra N. Lahiri, New York, Springer, 2006, 1 vol. (XVIII-618 p.), Springer Texts in Statistics, 0-387-32903-X • Measure Theory and Probability Theory, Texte imprimé, 9780387512655 • Measure Theory and Probability Theory, Texte imprimé, 9781441921918 • Measure theory and probability theory, Krishna B. Athreya, Soumendra N. Lahiri, New York, Springer, 2006, 1 vol. (XVIII-618 p.), Springer Texts in Statistics, 0-387-32903-X |
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| 082 | |a 519.2 | ||
| 100 | 1 | |a Athreya, Krishna Balasundaram, |d 1939- | |
| 245 | 1 | 0 | |a Measure theory and probability theory |c Krishna B. Athreya, Soumendra N. Lahiri. |
| 250 | |a 1st ed. 2006. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Texts in Statistics |x 2197-4136 | |
| 500 | |a Description d'après consultation du 11 avril 2011 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. [603]-609. Index | ||
| 505 | 1 | |a Measures and Integration: An Informal Introduction Measures Integration Lp-Spaces Differentiation Product Measures, Convolutions, and Transforms Probability Spaces Independence Laws of Large Numbers Convergence in Distribution Characteristic Functions Central Limit Theorems Conditional Expectation and Conditional Probability Discrete Parameter Martingales Markov Chains and MCMC Stochastic Processes Limit Theorems for Dependent Processes The Bootstrap Branching Processes | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended primarily for first year Ph.D. students in mathematics and statistics although mathematically advanced students from engineering and economics would also find the book useful. Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms. Thus part I would be particularly useful for students in a typical Statistics Ph.D. program if a separate course on real analysis is not a standard requirement. Part II (chapters 6-13) provides full coverage of standard graduate level probability theory. It starts with Kolmogorov's probability model and Kolmogorov's existence theorem. It then treats thoroughly the laws of large numbers including renewal theory and ergodic theorems with applications and then weak convergence of probability distributions, characteristic functions, the Levy-Cramer continuity theorem and the central limit theorem as well as stable laws. It ends with conditional expectations and conditional probability, and an introduction to the theory of discrete time martingales. Part III (chapters 14-18) provides a modest coverage of discrete time Markov chains with countable and general state spaces, MCMC, continuous time discrete space jump Markov processes, Brownian motion, mixing sequences, bootstrap methods, and branching processes. It could be used for a topics/seminar course or as an introduction to stochastic processes. Krishna B. Athreya is a professor at the departments of mathematics and statistics and a Distinguished Professor in the College of Liberal Arts and Sciences at the Iowa State University. He has been a faculty member at University of Wisconsin, Madison; Indian Institute of Science, Bangalore; Cornell University; and has held visiting appointments in Scandinavia and Australia. He is a fellow of the Institute of Mathematical Statistics USA; a fellow of the Indian Academy of Sciences, Bangalore; an elected member of the International Statistical Institute; and serves on the editorial board of several journals in probability and statistics. Soumendra N. Lahiri is a professor at the department of statistics at the Iowa State University. He is a fellow of the Institute of Mathematical Statistics, a fellow of the American Statistical Association, and an elected member of the International Statistical Institute | ||
| 650 | |a Théorie de la mesure | ||
| 650 | |a Probabilités | ||
| 700 | 1 | |a Lahiri, Soumendra Nath. |4 aut | |
| 700 | 1 | |a Lahiri, Soumendra N. |4 aut | |
| 776 | 0 | |0 109181433 |t Measure theory and probability theory |f Krishna B. Athreya, Soumendra N. Lahiri |c New York |n Springer |d 2006 |p 1 vol. (XVIII-618 p.) |s Springer Texts in Statistics |z 0-387-32903-X | |
| 776 | 0 | |t Measure Theory and Probability Theory |b Texte imprimé |z 9780387512655 | |
| 776 | 0 | |t Measure Theory and Probability Theory |b Texte imprimé |z 9781441921918 | |
| 776 | 0 | |0 109181433 |t Measure theory and probability theory |f Krishna B. Athreya, Soumendra N. Lahiri |c New York |n Springer |d 2006 |p 1 vol. (XVIII-618 p.) |s Springer Texts in Statistics |z 0-387-32903-X | |
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