An Advanced Course in Probability and Stochastic Processes

An Advanced Course in Probability and Stochastic Processes is a comprehensive textbook that covers probability theory and stochastic processes from a modern and rigorous perspective. It begins with measure theory and introduces key concepts such as probability, random variables, and stochastic processes, with full proofs and extensive examples. The book explores fundamental stochastic processes like Gaussian processes, Poisson random measures, Lévy processes, Markov processes, and Itô processes, emphasizing their interconnections. Special attention is given to martingales and the Wiener process, and the book includes numerous exercises to test and challenge the reader. It is suitable for students and researchers with a solid mathematical background and prior exposure to elementary probability and stochastic processes.

Format: Hardback
Length: 358 pages
Publication date: 15 December 2023
Publisher: Taylor & Francis Ltd

An in-depth exploration of probability theory and stochastic processes, this comprehensive textbook offers a modern and rigorous treatment suitable for upper undergraduate and graduate students. Starting with the foundations of measure theory, the book introduces key concepts of probability theory in an accessible manner, providing full proofs, extensive examples, and illustrations. Fundamental stochastic processes such as Gaussian processes, Poisson random measures, Lévy processes, Markov processes, and Itô processes are presented and explored in considerable depth, showcasing their many interconnections. Special attention is paid to martingales and the Wiener process, which play a central role in the treatment of stochastic integrals and stochastic calculus.

The book includes a wealth of exercises designed to test and challenge the reader, while also expanding their skillset. With its focus on mathematical understanding, rigorous and self-contained approach, accessibility, and comprehensive coverage, this textbook is an invaluable resource for students and researchers in the field.

Whether you are a mathematics student seeking to deepen your knowledge of probability and stochastic processes or a professional looking to advance your expertise, An Advanced Course in Probability and Stochastic Processes is an essential guide.

Weight: 860g
Dimension: 254 x 178 (mm)
ISBN-13: 9781032320465