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
Editore: American Mathematical Society, United States (2001)
ISBN 10: 0821828525 ISBN 13: 9780821828526
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Descrizione libro American Mathematical Society, United States, 2001. Paperback. Condizione libro: 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. Codice libro della libreria AAN9780821828526

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S.R.S Varadhan
Editore: American Mathematical Society, United States (2001)
ISBN 10: 0821828525 ISBN 13: 9780821828526
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Descrizione libro American Mathematical Society, United States, 2001. Paperback. Condizione libro: 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. Codice libro della libreria AAN9780821828526

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Descrizione libro American Mathematical Society, 2001. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria CE-9780821828526

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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218285260000000

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Descrizione libro American Mathematical Society. Paperback. Condizione libro: new. BRAND NEW, Probability Theory, S.R.S Varadhan, 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. Codice libro della libreria B9780821828526

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Varadhan, S.R.S (New York University, Courant Institute of Mathematical Sciences, USA)
Editore: American Mathematical Society (2001)
ISBN 10: 0821828525 ISBN 13: 9780821828526
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Descrizione libro American Mathematical Society, 2001. Condizione libro: 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. . . . . . . Codice libro della libreria V9780821828526

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Descrizione libro Paperback. Condizione libro: New. Not Signed; 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, book. Codice libro della libreria ria9780821828526_rkm

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Varadhan, S.R.S (New York University, Courant Institute of Mathematical Sciences, USA)
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Descrizione libro American Mathematical Society. Condizione libro: 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. . . . . . Books ship from the US and Ireland. Codice libro della libreria V9780821828526

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Descrizione libro Amer Mathematical Society, 2001. Paperback. Condizione libro: New. book. Codice libro della libreria 0821828525

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Descrizione libro Amer Mathematical Society, 2001. Paperback. Condizione libro: New. Codice libro della libreria DADAX0821828525

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