Measure Theory, Probability, and Stochastic Processes: 295 (Graduate Texts in Mathematics)

Book Details

• Publisher: Springer

• Author: Jean-François Le Gall

• Language: English

• Edition: 1st ed. 2022

• ISBN: 9783031142079

• Pages: 406

• Cover: Paperback

• Dimensions: 9.3 x 6.1 x 0.8 inches

About The Book

Measure Theory, Probability, and Stochastic Processes by Jean-François Le Gall provides an in-depth introduction to the foundational concepts of modern probability theory. Designed for readers with a working knowledge of real analysis, this textbook is a comprehensive guide to understanding the connections between probability theory and other areas of analysis.

The book is divided into three parts. The first part covers the essential concepts of measure theory, laying a strong foundation for probability. The second part introduces basic probability theory, discussing topics such as random variables, independence, conditional expectation, and various types of convergence. The third part delves into key stochastic processes, including discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter is followed by exercises of varying difficulty, providing readers with the opportunity to deepen their understanding.

This textbook is ideal for students seeking a solid grounding in probability theory and stochastic processes. It serves as an excellent introduction to the subject and offers a pathway to more advanced topics in stochastic processes, including those covered in Le Gall’s more advanced textbook in the same series. With its rigorous approach and clear explanations, this book is a valuable resource for anyone studying probability theory at an advanced level.