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Concept

Fractional Brownian motion

Related lectures (32)

Martingales and Brownian Motion Log in to Mediaspace to watch this video

Explores the concept of martingales and their relation to Brownian motion through symmetric simple random walks and discusses the potential positive outcomes from the current crisis.

Martingales and Brownian Motion Log in to Mediaspace to watch this video

Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.

Martingales and Brownian Motion: Part 1 Log in to Mediaspace to watch this video

Explores transformations of Brownian motion, Markov properties, and scaling invariance.

Martingales and Brownian Motion: Reflected and Absorbed Brownian Motion Log in to Mediaspace to watch this video

Explores the reflected and absorbed Brownian motion transformations and Markov properties.

Martingales and Brownian Motion Construction Log in to Mediaspace to watch this video

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

Stochastic Calculus: Brownian Motion Log in to Mediaspace to watch this video

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Martingales and Brownian Motion: Leaving Intervals and Maximum Distribution Log in to Mediaspace to watch this video

Explores the average time for a Brownian motion to leave an interval and the maximum distribution.

Hausdorff Dimension and Brownian Motion Log in to Mediaspace to watch this video

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 Log in to Mediaspace to watch this video

Explores the historical context and mathematical aspects of Brownian motion, including Einstein's model and experimental verification.

Hausdorff Dimension and Brownian Motion Log in to Mediaspace to watch this video

Explores the Hausdorff dimension of Brownian motion zeros, demonstrating a dimension of 1/2 with certainty.

Martingales and Brownian Motion Log in to Mediaspace to watch this video

Discusses the construction of random variables similar to Brownian motion and their implications.

Martingales and Brownian Motion: Reflection Principle Log in to Mediaspace to watch this video

Explores the reflection principle in martingales and Brownian motion, simplifying probability calculations.