Martingales and Brownian Motion: Drift and Exit Time

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Martingales and Brownian Motion

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

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.

Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Martingales and Brownian Motion: Construction and Properties

Explores the construction and properties of a Brownian motion with continuous trajectories using Paul Lévy's method.

Levy Flights & Brownian Motion

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

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.

Sub- and Supermartingales: Theory and Applications

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Stochastic Processes: Brownian Motion

Explores Brownian motion, Langevin equations, and stochastic processes in physics.

Fourier Transform and Spectral Densities

Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.