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Lecture
Martingales and Brownian Motion: Part 1
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Martingales and Brownian Motion: Reflected and Absorbed Brownian Motion
Explores the reflected and absorbed Brownian motion transformations and Markov properties.
Stopping Times: Martingales and Brownian Motion
Explores stopping times in martingales and Brownian motion, discussing convergence properties and the strong Markov property.
Martingales and Brownian Motion: Drift and Exit Time
Explores Brownian motion with drift, exit probabilities, and average exit times from intervals.
Martingales and Brownian Motion: Construction and Properties
Explores the construction and properties of a Brownian motion with continuous trajectories using Paul Lévy's method.
Martingales and Brownian Motion
Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.
Martingales and Brownian Motion
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.
Levy Flights & Brownian Motion
Explores Levy Flights and Brownian Motion, focusing on probability distributions and divergences in lag time.
Martingales and Brownian Motion Construction
Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.
Doob's Decomposition Theorem
Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.
Martingales and Brownian Motion: Global Behavior and Zero Set Length
Explores the behavior of Brownian motion and its zero set length.