Advanced Stochastic Processes by David Gamarnik
Advanced Stochastic Processes - Table of Contents
1. Metric spaces
2. Large Deviations Technique
3. Cramér’s Theorem
4. Applications of Large Deviations
5. LD in Many Dimensions and Markov Chains
6. Intro Brownian Motion
7. Brownian Motion
8. Quadratic Variation
9. Filtration and Martingales
10. Martingales I
11. Martingales II
12. Martingale Concentration Inequality
13. Talagrand’s Concentration Inequality
14. Itô Calculus
15. Itô Construction
16. Itô Integral
17. Itô Process and Formula
18. Integration with Respect to Martingales
19. Itô Applications
20. Weak Convergence
21. Tightness of Measures
22. Reflected Brownian Motion
What You Will Learn in Advanced Stochastic Processes
Advanced Stochastic Processes by David Gamarnik is a graduate-level course material from MIT that focuses on advanced topics in stochastic processes and probability theory. It is designed for students who already have a strong background in mathematics and want to study how random systems evolve over time using rigorous mathematical tools.
The course covers key concepts such as Markov processes, martingales, Brownian motion, Itô calculus, and stochastic differential equations. It also introduces more advanced ideas like large deviations theory, stopping times, and reflected Brownian motion, which are important in modern probability and applied mathematics. These topics help explain complex random behavior in systems studied in science, engineering, and economics.
A major strength of this material is its connection between theory and real-world applications. It shows how stochastic modeling is used in areas such as finance, queueing systems, and operations research. Overall, this course provides a strong foundation in advanced stochastic analysis, making it valuable for graduate students and researchers working with probabilistic and dynamic systems.
Book Details & Specifications
Title:
Advanced Stochastic Processes by David Gamarnik
Publisher:
Massachusetts Institute of Technology
Year:
213
Pages:
322
Type:
PDF
Language:
English
ISBN-10 #:
103232046X
ISBN-13 #:
978-1032320465
License:
External Educational Resource
Amazon:
Amazon
About the Author: David Gamarnik
The author
David Gamarnik
is a Georgian-born American mathematician and professor at MIT (Massachusetts Institute of Technology). He earned his B.Sc. in Mathematics from New York University and completed his PhD in Operations Research at MIT. His academic background is strongly rooted in advanced mathematics and probability.
His expertise includes stochastic processes, probability theory, random graphs, optimization, and machine learning. He is known for research in queueing theory, stochastic modeling, and discrete probability, with applications in data science, computer science, and complex systems, making him a leading figure in applied probability and advanced stochastic processes.
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