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Fractional Brownian motion
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Doob's Decomposition Theorem
Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.
Introduction to Data Science
Introduces data science topics, evaluation methods, and course organization for the semester.
Brownian Motion: Modeling and Analysis
Explores the analysis of Brownian motion through different models and Markov processes.
Brownian Motion: Theory and Applications
Covers the theory of Brownian motion, diffusion, and random walks, with a focus on Einstein's theory for one-dimensional motion.
Martingales and Brownian Motion: Leaving Intervals and Maximum Distribution
Explores the average time for a Brownian motion to leave an interval and the maximum distribution.
Hausdorff Dimension and Brownian Motion
Explores Hausdorff dimension and its application to Brownian motion sets, emphasizing the importance of understanding set dimensions in stochastic processes.
Brownian Motion: Historical Background and Mathematical Construction
Explores the historical context and mathematical aspects of Brownian motion, including Einstein's model and experimental verification.
Hausdorff Dimension and Brownian Motion
Explores the Hausdorff dimension of Brownian motion zeros, demonstrating a dimension of 1/2 with certainty.
Martingales and Brownian Motion
Discusses the construction of random variables similar to Brownian motion and their implications.
Martingales and Brownian Motion: Reflection Principle
Explores the reflection principle in martingales and Brownian motion, simplifying probability calculations.
