INTRODUCTION TO PROBABILITY THEORY

This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it.The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability language. The second part is devoted to some more sophisticated methods such as conditional expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part. --Contents:

• Preface
• About the Author
• Acknowledgments
• The Modern Probability Language:
  • Elements of Combinatorial Analysis and Simple Random Walks
  • The Modern Probability Language
• Conditional Expectations, Martingales and Markov Chains:
  • Conditional Expectations
  • Martingales
  • Markov Chains
• Appendices:
  • Basics of Measure Theory
  • Basics of Integration Theory
• Bibliography
• Index

Readership: Undergraduate students in mathematics and physics majors, particularly those taking any first course in probability theory. Undergraduate students in economy, finance, engineering or any other subject that includes probability theory in the curriculum (e.g., biology, chemistry).Probability Theory;Measure Theory;Stochastic Processes;Probability Distributions;Expectation Values;Conditional Expectation Values;Markov Processes;Martingales00