Martingales and Brownian Motion: Construction and Properties

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Martingales and Brownian Motion Construction

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

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.

Martingales and Brownian Motion: Drift and Exit Time

Explores Brownian motion with drift, exit probabilities, and average exit times from intervals.

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

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

Levy Flights & Brownian Motion

Explores Levy Flights and Brownian Motion, focusing on probability distributions and divergences in lag time.

Martingales and Brownian Motion: Global Behavior and Zero Set Length

Explores the behavior of Brownian motion and its zero set length.

Martingales and Brownian Motion: Part 1

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

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Martingale Convergence Theorem: Proof and Recap

Covers the proof and recap of the martingale convergence theorem, focusing on the conditions for the existence of a random variable.