**Student Mathematical Library**

Volume: 38;
2007;
252 pp;
Softcover

MSC: Primary 60;

**Print ISBN: 978-0-8218-4333-8
Product Code: STML/38**

List Price: $45.00

Individual Price: $36.00

**Electronic ISBN: 978-1-4704-1216-6
Product Code: STML/38.E**

List Price: $42.00

Individual Price: $33.60

#### Supplemental Materials

# Filtering and Prediction: A Primer

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*B. Fristedt; N. Jain; N. Krylov*

Filtering and prediction is about observing moving objects when the
observations are corrupted by random errors. The main focus is then on
filtering out the errors and extracting from the observations the most
precise information about the object, which itself may or may not be moving
in a somewhat random fashion. Next comes the prediction step where, using
information about the past behavior of the object, one tries to predict
its future path.

The first three chapters of the book deal with discrete probability
spaces, random variables, conditioning, Markov chains, and filtering
of discrete Markov chains. The next three chapters deal with the more
sophisticated notions of conditioning in nondiscrete situations,
filtering of continuous-space Markov chains, and of Wiener
process. Filtering and prediction of stationary sequences is discussed
in the last two chapters.

The authors believe that they have succeeded in presenting necessary ideas
in an elementary manner without sacrificing the rigor too much. Such
rigorous treatment is lacking at this level in the literature. In the past
few years the material in the book was offered as a one-semester
undergraduate/beginning graduate course at the University of Minnesota. Some
of the many problems suggested in the text were used in homework
assignments.

#### Readership

Undergraduate and graduate students interested in filtering and prediction for random processes.

#### Reviews & Endorsements

The book is written in an elementary way but it is still mathematically rigorous. The book can be recommended to all students interested in stochastic models.

-- EMS Newsletter

The book is well-written and provides a very nice basis for lecturing about this topic.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Filtering and Prediction: A Primer

- Cover Cover11
- Title iii4
- Copyright iv5
- Contents v6
- Preface ix10
- Chapter 1. Preliminaries 114
- Chapter 2. Markov chains 3346
- Chapter 3. Filtering of discrete Markov chains 6174
- Chapter 4. Conditional expectations 95108
- Chapter 5. Filtering of continuous-space Markov chains 127140
- Chapter 6. Wiener process and continuous time filtering 161174
- Chapter 7. Stationary sequences 191204
- Chapter 8. Prediction of stationary sequences 225238
- Bibliography 247260
- Index 249262
- Back Cover Back Cover1266