Lectures related to Martingales and Brownian Motion

Fourier Transform and Spectral Densities

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

Maximum Entropy Principle: Stochastic Differential Equations

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

Stochastic Processes: Brownian Motion

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

White Noise Form of the Langevin Equation

Covers the white noise form of the Langevin equation and its applications.

Sub- and Supermartingales: Theory and Applications

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

Stochastic Calculus: Interest Rate Models

Provides an overview of stochastic calculus and its applications in interest rate models and financial modeling.

Quadratic Variation: Martingales and Stochastic Integrals

Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.

Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Martingale Convergence Theorem

Explains the martingale convergence theorem and its applications in probability theory.

Linear Response and Complex Diffusivity

Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.

Brownian Motion: From Molecules to Cells

Explores the core concepts of Brownian motion, from molecules to cells, including its history, hypothesis versus description, Langevin's solution, and methods for measuring Brownian motion.

Martingales and Stochastic Integration

Covers martingales, stochastic integration, and localizing processes using stopping times.

Stochastic Differential Equations

Covers Stochastic Differential Equations, Wiener increment, Ito's lemma, and white noise integration in financial modeling.

Brownian Motion: Fundamentals and Applications

Covers the fundamentals of Brownian motion and its applications in various fields.

Stochastic Calculus: Itô's Formula Log in to Mediaspace to watch this video

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

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 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.

Martingales and Brownian Motion: Convergence Criteria and Theorems Log in to Mediaspace to watch this video

Explores convergence criteria for martingales, including almost sure convergence and Cauchy criterion, leading to the first martingale convergence theorem.

Martingales and Brownian Motion: Drift and Exit Time Log in to Mediaspace to watch this video

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

Stochastic Calculus: Integrals and Processes Log in to Mediaspace to watch this video

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.