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Title
Measure theory, probability, and stochastic processes / Jean-François Le Gall.
ISBN
9783031142055 (electronic bk.)
3031142055 (electronic bk.)
3031142047
9783031142048
Published
Cham, Switzerland : Springer, 2022.
Language
English
Description
1 online resource : illustrations (black and white, and color).
Item Number
10.1007/978-3-031-14205-5 doi
Call Number
QA312
Dewey Decimal Classification
515/.42
Summary
This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis. Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix. Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the authors more advanced textbook in the same series (GTM 274).
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Graduate texts in mathematics ; 295.
Part I. Measure Theory
Chapter 1. Measurable Spaces
Chapter 2. Integration of Measurable Functions
Chapter 3. Construction of Measures
Chapter 4. Lp Spaces
Chapter 5. Product Measure
Chapter 6. Signed Measures
Chapter 7. Change of Variables
Part II. Probability Theory
Chapter 8. Foundations of Probability Theory
Chapter 9. Independence
Chapter 10. Convergence of Random Variables
Chapter 11. Conditioning
Part III. Stochastic Processes
Chapter 12. Theory of Martingales
Chapter 13. Markov Chains
Chapter 14. Brownian Motion.
