Probability Theory

S.R.S Varadhan

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Lingua: inglese

Editore: American Mathematical Society, US, 2001

0821828525 / 9780821828526

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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. …

Codice articolo LU-9780821828526

Titolo
Probability Theory
Autore
S.R.S Varadhan
Editore
American Mathematical Society, US
Anno di pubblicazione
2001
Condizione
New
Rilegatura
Paperback
Lingua
inglese
ISBN 10
0821828525
ISBN 13
9780821828526
Peso dell'articolo
329 grammi
Dimensioni
18.42 x 1.27 x 26.04 cm

Rarewaves.com USA

London, London, Regno Unito

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Venditore AbeBooks dal 11 giugno 2025

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