A modern approach to probability theory

Author(s)

• Fristedt, Bert
• Gray, Lawrence F.

Bibliographic Information

A modern approach to probability theory

Bert Fristedt, Lawrence Gray

（Probability and its applications）

Birkhäuser, c1997

• : us : hbk
• : sz : hbk

Note

Includes bibliographical references and index

Description and Table of Contents

Volume

: us : hbk ISBN 9780817638078

Description

Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications-Bayesian statistics, financial mathematics, information theory, tomography, and signal processing-appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

Table of Contents

List of Tables * Preface * Part I: Probability Spaces, Random Variables, and Expectations * Probability Spaces * Random Variables * Distribution Functions * Expectations: Theory * Expectations: Applications * Calculating Probabilities and Measures * Measure Theory: Existence and Uniqueness * Integration Theory * Part 2: Independence and Sums * Stochastic Independence * Sums of Independent Random Variables * Random Walk * Theorems of A.S. Convergence * Characteristic Functions * Part 3: Convergence in Distribution * Convergence in Distribution on the Real Line * Distributional Limit Theorems for Partial Sums * Infinitely Divisible and Stable Distributions as Limits * Convergence in Distribution on Polish Spaces * The Invariance Principle and Brownian Motion * Part 4: Conditioning * Spaces of Random Variables * Conditional Probabilities * Construction of Random Sequences * Conditional Expectations * Part 5: Random Sequences * Martingales * Renewal Sequences * Time-homogeneous Markov Sequences * Exchangeable Sequences * Stationary Sequences * Part 6: Stochastic Processes * Point Processes * Diffusions and Stochastic Calculus * Applications of Stochastic Calculus * Part 7: Appendices * Appendix A. Notation and Usage of Terms * Appendix B. Metric Spaces * Appendix C. Topological Spaces * Appendix D. Riemann-Stieltjes Integration * Appendix E. Taylor Approximations, C-Valued Logarithms * Appendix F. Bibliography * Appendix G. Comments and Credits * Index

Volume

: sz : hbk ISBN 9783764338077

Description

This textbok is designed for graduate students in probability theory. It merges measure theory with probability theory, and rather than deal only with "random variables" it also looks at "random objects". There is a chapter of introductory material for advanced topics, as well as over 1000 exercises, ranging from gambling theory to concrete calculations involving random sets. All of the problems in the exercises are designed to help students get beyond mere rote learning of theorems and proofs to a deep intuitive feel for the far-reaching implications of the theory. Solutions are provided for approximately a quarter of the exercises.

by "Nielsen BookData"

Details

• NCID: BA29207354
• ISBN:
  • 0817638075
  • 3764338075
• LCCN: 96005687
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boston
• Pages/Volumes: xx, 756 p.
• Size: 25 cm
• Classification:
  • NDC9 : 417.1
  • LCC : QA273
  • DC20 : 519.2
• Subject Headings:
  • LCSH : Probabilities
• Parent Bibliography ID:
  • BA10668227