Softcover ISBN:  9780821840856 
Product Code:  CLN/16 
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Electronic ISBN:  9781470431167 
Product Code:  CLN/16.E 
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Book DetailsCourant Lecture NotesVolume: 16; 2007; 126 ppMSC: Primary 60;
This is a brief introduction to stochastic processes studying certain elementary continuoustime processes. After a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps, the author proceeds to introduce Brownian motion and to develop stochastic integrals and Itô's theory in the context of onedimensional diffusion processes. The book ends with a brief survey of the general theory of Markov processes.
The book is based on courses given by the author at the Courant Institute and can be used as a sequel to the author's successful book Probability Theory in this series.
Srinivasa S. R. 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.ReadershipGraduate students and research mathematicians interested in stochastic processes.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Processes with independent increments

Chapter 3. Poisson point processes

Chapter 4. Jump Markov processes

Chapter 5. Brownian motion

Chapter 6. Onedimensional diffusions

Chapter 7. General theory of Markov processes

Appendix A. Measures on Polish spaces

Appendix B. Additional remarks


Additional Material

Reviews

The text is one of those that may be strongly recommended to all young mathematicians as a starter to precede a deeper study of probability and stochastic processes.
EMS Newsletter 
Amazingly, almost all of the proofs are given explicitly. In fact the author provides only eight references in the bibliography. This reflects the fact that, as a whole, this book is written in a totally selfcontained manner. ...I can say that this book is a set of very wellwritten lecture notes, and it is organized as a clear synthesis of the theory of continuoustime stochastic processes with many examples and with plenty of exercises...
Mathematical Reviews


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 Book Details
 Table of Contents
 Additional Material
 Reviews

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This is a brief introduction to stochastic processes studying certain elementary continuoustime processes. After a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps, the author proceeds to introduce Brownian motion and to develop stochastic integrals and Itô's theory in the context of onedimensional diffusion processes. The book ends with a brief survey of the general theory of Markov processes.
The book is based on courses given by the author at the Courant Institute and can be used as a sequel to the author's successful book Probability Theory in this series.
Srinivasa S. R. 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.
Graduate students and research mathematicians interested in stochastic processes.

Chapters

Chapter 1. Introduction

Chapter 2. Processes with independent increments

Chapter 3. Poisson point processes

Chapter 4. Jump Markov processes

Chapter 5. Brownian motion

Chapter 6. Onedimensional diffusions

Chapter 7. General theory of Markov processes

Appendix A. Measures on Polish spaces

Appendix B. Additional remarks

The text is one of those that may be strongly recommended to all young mathematicians as a starter to precede a deeper study of probability and stochastic processes.
EMS Newsletter 
Amazingly, almost all of the proofs are given explicitly. In fact the author provides only eight references in the bibliography. This reflects the fact that, as a whole, this book is written in a totally selfcontained manner. ...I can say that this book is a set of very wellwritten lecture notes, and it is organized as a clear synthesis of the theory of continuoustime stochastic processes with many examples and with plenty of exercises...
Mathematical Reviews