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Probability Theory
 
S. R. S. Varadhan New York University - Courant Institute of Mathematical Sciences, New York, NY
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Probability Theory
Softcover ISBN:  978-0-8218-2852-6
Product Code:  CLN/7
List Price: $30.00
MAA Member Price: $27.00
AMS Member Price: $24.00
eBook ISBN:  978-1-4704-1137-4
Product Code:  CLN/7.E
List Price: $28.00
MAA Member Price: $25.20
AMS Member Price: $22.40
Softcover ISBN:  978-0-8218-2852-6
eBook: ISBN:  978-1-4704-1137-4
Product Code:  CLN/7.B
List Price: $58.00 $44.00
MAA Member Price: $52.20 $39.60
AMS Member Price: $46.40 $35.20
Probability Theory
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Probability Theory
S. R. S. Varadhan New York University - Courant Institute of Mathematical Sciences, New York, NY
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Softcover ISBN:  978-0-8218-2852-6
Product Code:  CLN/7
List Price: $30.00
MAA Member Price: $27.00
AMS Member Price: $24.00
eBook ISBN:  978-1-4704-1137-4
Product Code:  CLN/7.E
List Price: $28.00
MAA Member Price: $25.20
AMS Member Price: $22.40
Softcover ISBN:  978-0-8218-2852-6
eBook ISBN:  978-1-4704-1137-4
Product Code:  CLN/7.B
List Price: $58.00 $44.00
MAA Member Price: $52.20 $39.60
AMS Member Price: $46.40 $35.20
  • Book Details
     
     
    Courant Lecture Notes
    Volume: 72001; 167 pp
    MSC: Primary 60;

    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.

    S. R. S. Varadhan is the winner of the 2007 Abel Prize. Varadhan was awarded the prize "for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations". Read more here.

    Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

    Readership

    Graduate students and research mathematicians interested in probability theory and stochastic processes and in applications to economics, and finance.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Measure theory
    • Chapter 2. Weak convergence
    • Chapter 3. Independent sums
    • Chapter 4. Dependent random variables
    • Chapter 5. Martingales
    • Chapter 6. Stationary stochastic processes
    • Chapter 7. Dynamic programming and filtering
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 72001; 167 pp
MSC: Primary 60;

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.

S. R. S. Varadhan is the winner of the 2007 Abel Prize. Varadhan was awarded the prize "for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations". Read more here.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Readership

Graduate students and research mathematicians interested in probability theory and stochastic processes and in applications to economics, and finance.

  • Chapters
  • Chapter 1. Measure theory
  • Chapter 2. Weak convergence
  • Chapter 3. Independent sums
  • Chapter 4. Dependent random variables
  • Chapter 5. Martingales
  • Chapter 6. Stationary stochastic processes
  • Chapter 7. Dynamic programming and filtering
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.