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An advanced course in probability and stochastic processes

Author: Kroese, D. P., & Botev, Z.

Published: 2024

Call Number: GS 519.2 K913 2024

Posted on: November 12, 2025


About this Book:
This book provides a modern and rigorous treatment of probability theory and stochastic processes at an upper undergraduate and graduate level. Starting with the foundations of measure theory, it introduces the key concepts of probability theory in an accessible way, providing full proofs and extensive examples, and illustrations. Fundamental stochastic processes such as Gaussian processes, Poisson random measures, Lâevy processes, Markov processes, and Itão processes are presented and explored in considerable depth, showcasing their many interconnections. Special attention is paid to martingales and the Wiener process and their central role in the treatment of stochastic integrals and stochastic calculus. The presented material includes many exercises, designed to test and challenge the reader and expand their skillset. An Advanced Course in Probability and Stochastic Processes is meant for students and researchers who have a solid mathematical background.