Probability Theory
S.R.S Varadhan
Sold by Rarewaves.com USA, London, LONDO, United Kingdom
AbeBooks Seller since June 11, 2025
New - Soft cover
Condition: New
Ships from United Kingdom to U.S.A.
Quantity: 2 available
Add to basketSold by Rarewaves.com USA, London, LONDO, United Kingdom
AbeBooks Seller since June 11, 2025
Condition: New
Quantity: 2 available
Add to basketThis 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.
Seller Inventory # LU-9780821828526
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.
Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
"About this title" may belong to another edition of this title.
Please note that we do not offer Priority shipping to any country.
We currently do not ship to the below countries:
Russia
Belarus
Ukraine
Israel
Please do not attempt to place orders with any of these countries as a ship to address - they will be cancelled.
| Order quantity | 10 to 15 business days | 10 to 15 business days |
|---|---|---|
| First item | US$ 0.00 | US$ 0.00 |
Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.