Measure Theory, Probability, and Stochastic Processes

This textbook provides an introduction to modern probability theory,highlighting the connections between probability and other areas of analysis. It begins with a rigorous treatment of measure theory and covers random variables,independence,conditional expectation,and convergence. The third part discusses stochastic processes,including discrete-time martingales,countable state-space Markov chains,and Brownian motion. Each chapter ends with exercises.

Format: Hardback
Length: 406 pages
Publication date: 30 October 2022
Publisher: Springer International Publishing AG

This comprehensive textbook offers a thorough introduction to modern probability theory, catering to readers with a solid foundation in real analysis. By emphasizing the connections between martingales, Markov chains, Brownian motion, and harmonic functions, it provides a comprehensive overview of the intricate interplay between probability and various branches of analysis. The book is organized into three parts, beginning with a rigorous treatment of measure theory, which serves as a foundation for probability concepts. The second part delves into fundamental probability principles, including random variables, independence, conditional expectation, and various types of convergence of random variables. In the third part, readers are introduced to three crucial classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter concludes with a selection of challenging exercises to reinforce the understanding of the material. Additionally, an appendix provides essential background information from functional analysis, particularly focusing on Hilbert and Banach spaces.

This textbook is particularly valuable for students seeking a comprehensive understanding of basic probability theory. It serves as a solid foundation for those interested in exploring further topics in Brownian motion and other continuous-time stochastic processes, as recommended by the authors in the same series (GTM 274). Whether you are a mathematics student, a researcher in probability or statistics, or simply someone passionate about understanding the principles of probability, this textbook will provide you with the necessary tools and insights to advance your knowledge in this field.

Weight: 806g
Dimension: 160 x 242 x 27 (mm)
ISBN-13: 9783031142048
Edition number: 1st ed. 2022