Softcover ISBN:  9780821843338 
Product Code:  STML/38 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470412166 
Product Code:  STML/38.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821843338 
eBook: ISBN:  9781470412166 
Product Code:  STML/38.B 
List Price:  $108.00 $83.50 
Softcover ISBN:  9780821843338 
Product Code:  STML/38 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470412166 
Product Code:  STML/38.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821843338 
eBook ISBN:  9781470412166 
Product Code:  STML/38.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 38; 2007; 252 ppMSC: Primary 60
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 continuousspace 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 onesemester undergraduate/beginning graduate course at the University of Minnesota. Some of the many problems suggested in the text were used in homework assignments.
ReadershipUndergraduate and graduate students interested in filtering and prediction for random processes.

Table of Contents

Chapters

Chapter 1. Preliminaries

Chapter 2. Markov chains

Chapter 3. Filtering of discrete Markov chains

Chapter 4. Conditional expectations

Chapter 5. Filtering of continuousspace Markov chains

Chapter 6. Wiener process and continuous time filtering

Chapter 7. Stationary sequences

Chapter 8. Prediction of stationary sequences


Additional Material

Reviews

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 wellwritten and provides a very nice basis for lecturing about this topic.
Zentralblatt MATH


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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 continuousspace 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 onesemester undergraduate/beginning graduate course at the University of Minnesota. Some of the many problems suggested in the text were used in homework assignments.
Undergraduate and graduate students interested in filtering and prediction for random processes.

Chapters

Chapter 1. Preliminaries

Chapter 2. Markov chains

Chapter 3. Filtering of discrete Markov chains

Chapter 4. Conditional expectations

Chapter 5. Filtering of continuousspace Markov chains

Chapter 6. Wiener process and continuous time filtering

Chapter 7. Stationary sequences

Chapter 8. Prediction of stationary sequences

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 wellwritten and provides a very nice basis for lecturing about this topic.
Zentralblatt MATH