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A Probability Path

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Synopses & Reviews

Publisher Comments:

Many probability books are written by mathematicians and have the built in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.

Synopsis:

This text is geared towards students who have no prior exposure to measure theory or advanced probability, and who require this material for their work in statistics, applied probability, operations research, mathematical finance, and engineering.

A one semester path is laid out in an efficient and disciplined way to cover the core material. The first three chapters provide a functioning knowledge of measure theory, Chapter 4 discusses independence, with expectation and integration covered in Chapter 5. This is followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation) and applied probability. The remaining chapters offer a careful treatment of convergence in distribution and the central limit theorem. Finally, the text treats conditional expectation and martingales, closing on the fundamental theorem of mathematical finance.

Table of Contents

1. Sets and Events ; 2. Probability Spaces; 3. Random Variables, Elements and Measurable Maps; 4. Independence; 5. Integration and Expectation; 6. Convergence Concepts; 7. Laws of Large Numbers and Sums of Independent Random Variables; 8. Convergence in Distribution; 9. Characteristic Functions and the Central Limit Theorem; 10. Martingales; Index; References

Product Details

ISBN:
9780817640552
Author:
Resnick, Sidney
Author:
Resnick, S.
Publisher:
Birkhauser
Location:
Boston, MA
Subject:
Probability
Subject:
Probabilities
Subject:
Stochastic processes
Subject:
Probability & Statistics - General
Subject:
Statistics
Subject:
Probability Theory and Stochastic Processes
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Operations Research, Mathematical Programming
Subject:
Statistical Theory and Methods
Subject:
Operations Research, Management Science
Subject:
Mathematics | Probability and Statistics
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Subject:
Mathematical statistics
Copyright:
Edition Description:
1st ed. 1998. 3rd printing
Publication Date:
19981223
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
466
Dimensions:
235 x 155 mm 1840 gr

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Related Subjects


Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

A Probability Path New Hardcover
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Product details 466 pages Birkhauser Boston - English 9780817640552 Reviews:
"Synopsis" by , This text is geared towards students who have no prior exposure to measure theory or advanced probability, and who require this material for their work in statistics, applied probability, operations research, mathematical finance, and engineering.

A one semester path is laid out in an efficient and disciplined way to cover the core material. The first three chapters provide a functioning knowledge of measure theory, Chapter 4 discusses independence, with expectation and integration covered in Chapter 5. This is followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation) and applied probability. The remaining chapters offer a careful treatment of convergence in distribution and the central limit theorem. Finally, the text treats conditional expectation and martingales, closing on the fundamental theorem of mathematical finance.

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