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Related lectures (32)

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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.