Information

• Versions (taught during): ML-2018, FinTech-2018 (Spring 2018)
• Venue: Higher School of Economics
• Taught for: Bachelor Students in Machine Learning, Math & Finance

Abstract

This course provides an introduction into stochastic processes, fundamental to understanding randomness and uncertainty in various systems. We start with the theoretical underpinnings of stochastic processes, including Wiener and Poisson type processes, Markov chains, and Markov processes. Practical aspects such as generating realizations of random processes will also be covered. Advanced topics will include Gaussian and conditional Gaussian models, Hidden Markov Models, and multivariate Gaussian estimation using techniques such as the Kalman filter. The course will also touch upon decision theory, introducing key statistics and tests crucial for making informed decisions in uncertain environments. More practical applications such as anomaly and change-point detection will be considered, demonstrating the relevance of stochastic processes in addressing real-world challenges across various domains.

Course Contents

• Lecture 1. Stochastic processes and their characteristics.
• Lecture 2. Theory fundamentals of stochastic processes.
• Lecture 3. Wiener and Poisson type processes. Generation of realizations of random processes.
• Lecture 4. Markov chains.
• Lecture 5. Markov processes.
• Lecture 6. Stochastic models with discrete time.
• Lecture 7. Gaussian and conditional Gaussian models.
• Lecture 8. Hidden Markov models.
• Lecture 9. Multivariate Gaussian estimation. Kalman filter.
• Lecture 10. Key statistics and tests in decision theory.
• Lecture 11. Anomaly detection. Change-point detection.
• Lecture 12. Financial time series and empirical facts about them.