Lectures related to Wiener process

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

Wiener Process: Definition and Properties

Explains the definition and properties of the Wiener process, focusing on its covariance function and continuous paths.

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.

Stochastic Calculus: Itô's Formula

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

Stochastic Differential Equations

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

Stochastic Calculus: Integrals and Processes

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

Girsanov's Theorem: Numerical Simulation of SDEs

Covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs) with applications in finance.

Fokker-Planck Equation: Derivations and Applications

Explores the derivation of the Fokker-Planck equation and its applications in stochastic differential equations.

Sub- and Supermartingales: Theory and Applications

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

Levy Flights & Brownian Motion

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

White Noise Form of the Langevin Equation

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

Fourier Transform and Spectral Densities

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

Stochastic Optimal Control: Martingale Theorem

Explores Stochastic Optimal Control, emphasizing Optimal Consumption and Investment, the Martingale Representation Theorem, and the Verification Theorem.

Stochastic Processes: Brownian Motion

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

Martingales and Brownian Motion: Global Behavior and Zero Set Length

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

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.

Fokker-Planck Equations

Explores Fokker-Planck equations, escape rates, and first passage time analysis in statistical physics.

Maximum Entropy Principle: Stochastic Differential Equations

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

The Black-Scholes-Merton Model

Covers the Black-Scholes-Merton model, dynamics, self-financing strategies, and the PDE.

Martingales and Brownian Motion: Construction and Properties

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