This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation. In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. ...
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This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation. In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Then both the weak and strong limit theorems for sums of independent random variables are proved, including the weak and strong laws of large numbers, central limit theorems, laws of the iterated logarithm, and the Kolmogorov three series theorem. The first part concludes with infinitely divisible distributions and limit theorems for sums of uniformly infinitesimal independent random variables. The second part of the book mainly deals with dependent random variables, particularly martingales and Markov chains. Topics include standard results regarding discrete parameter martingales and Doob's inequalities. The standard topics in Markov chains are treated, i.e., transience, and null and positive recurrence. A varied collection of examples is given to demonstrate the connection between martingales and Markov chains. Additional topics covered in the book include stationary Gaussian processes, ergodic theorems, dynamic programming, optimal stopping, and filtering. A large number of examples and exercises is included. The book is a suitable text for a first-year graduate course in probability.
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Add this copy of Probability Theory (Courant Lecture Notes) to cart. $22.61, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 2001 by Amer Mathematical Society.
Publisher:
Courant Institute of Mathemetical Sciences
Published:
2001
Language:
English
Alibris ID:
18251619486
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Publisher:
Courant Institute of Mathemetical Sciences
Published:
2001
Language:
English
Alibris ID:
18236195003
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This item is in overall good condition. Covers and dust jackets are intact but may have minor wear including slight curls or bends to corners as well as cosmetic blemishes including stickers. Pages are intact but may have minor highlighting/ writing. Binding is intact; however, spine may have slight wear overall. Digital codes may not be included and have not been tested to be redeemable and/or active. Minor shelf wear overall. Please note that all items are donated goods and are in used condition. Orders shipped Monday through Friday! Your purchase helps put people to work and learn life skills to reach their full potential. Orders shipped Monday through Friday. Your purchase helps put people to work and learn life skills to reach their full potential. Thank you!
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Publisher:
Courant Institute of Mathemetical Sciences
Published:
2001
Language:
English
Alibris ID:
18236857178
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New. 2001. Paperback. This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including all the standard topics. Series: Courant Lecture Notes. Num Pages: 167 pages, bibliography, index. BIC Classification: PBT; PBWL. Category: (P) Professional & Vocational. Dimension: 252 x 177 x 10. Weight in Grams: 326......We ship daily from our Bookshop.
Add this copy of Probability Theory to cart. $53.86, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2001 by Courant Institute of Mathemetical Sciences.
