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Related lectures (32)

Optional Stopping Theorem: Proof and Applications

Covers the optional stopping theorem for martingales, providing a detailed proof and discussing its implications.

Conditional Gaussian Generation

Explores the generation of multivariate Gaussian distributions and the challenges of factorizing covariance matrices.

Fourier Transform and Spectral Densities

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

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: Three Stopping Theorems

Explores three stopping theorems in martingales and Brownian motion.

Sub- and Supermartingales: Theory and Applications

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

Doob's Decomposition Theorem

Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.

Optional Stopping Theorem

Explores stopping times, the optional stopping theorem, F-measurable random variables, and 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: Construction and Properties

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

Martingale Convergence Theorem: Proof and Stopping Time

Explores the proof of the martingale convergence theorem and the concept of stopping time in square-integrable martingales.

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: Global Behavior and Zero Set Length

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

Martingales and Brownian Motion Construction

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

Optional Stopping Theorem: Martingales and Stepping Times

Explores the optional stopping theorem for martingales and stepping times, emphasizing its applications and implications.

Maximum Entropy Principle: Stochastic Differential Equations

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

Martingale Convergence Theorem

Covers the proof of the martingale convergence theorem and the convergence of the martingale sequence almost surely.

Stopping Times: Martingales and Brownian Motion

Explores stopping times in martingales and Brownian motion, discussing convergence properties and the strong Markov property.

Reflection Principle: Proof and Observations

Covers the reflection principle and martingale writing in simple symmetric random walks.

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