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Full Description
An Advanced Course in Probability and Stochastic Processes 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, this book 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, 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 and their central role in the treatment of stochastic integrals and stochastic calculus. This book 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 and who have had prior exposure to elementary probability and stochastic processes.
Key Features:
Focus on mathematical understanding
Rigorous and self-contained
Accessible and comprehensive
High-quality illustrations
Includes essential simulation algorithms
Extensive list of exercises and worked-out examples
Elegant and consistent notation
Contents
1. Measure Theory 2. Probability 3. Convergence 4. Conditioning 5. Martingales 6. Wiener and Brownian Motion Processes 7. Itô Calculus Appendix A. Selected Solutions Appendix B. Function Spaces Appendix C. Existence of the Lebesgue Measure Index
