Probability Theory (Courant Lecture Notes)

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9780821828526: Probability Theory (Courant Lecture Notes)

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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1.

S.R.S Varadhan
Editorial: American Mathematical Society, United States (2001)
ISBN 10: 0821828525 ISBN 13: 9780821828526
Nuevos Paperback Cantidad: 1
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The Book Depository
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 2001. Paperback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AAN9780821828526

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2.

S. R. S. Varadhan
Editorial: Courant Institute of Mathemetical Sciences (2001)
ISBN 10: 0821828525 ISBN 13: 9780821828526
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Descripción Courant Institute of Mathemetical Sciences, 2001. Paperback. Estado de conservación: New. Brand new. We distribute directly for the publisher. S. R. S. Varadhan is recognized as a top expert in probability theory. This volume presents topics in probability theory covered during a first-year graduate course given by Varadhan 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. Nº de ref. de la librería 1007090084

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3.

S.R.S Varadhan
Editorial: American Mathematical Society, United States (2001)
ISBN 10: 0821828525 ISBN 13: 9780821828526
Nuevos Paperback Cantidad: 1
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The Book Depository US
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 2001. Paperback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AAN9780821828526

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Varadhan, S. R. S.
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ISBN 10: 0821828525 ISBN 13: 9780821828526
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Descripción Amer Mathematical Society. Estado de conservación: Brand New. Ships from USA. FREE domestic shipping. Nº de ref. de la librería 0821828525

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Descripción American Mathematical Society, 2001. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería CE-9780821828526

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Descripción Amer Mathematical Society, 2001. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0821828525

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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97808218285260000000

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Descripción Estado de conservación: New. Bookseller Inventory # ST0821828525. Nº de ref. de la librería ST0821828525

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Descripción Amer Mathematical Society, 2001. Paperback. Estado de conservación: Brand New. 167 pages. 10.25x7.25x0.50 inches. In Stock. Nº de ref. de la librería __0821828525

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Descripción Amer Mathematical Society, 2001. Paperback. Estado de conservación: New. Nº de ref. de la librería DADAX0821828525

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