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Stochastic processses

Related lectures (32)

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

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

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

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

Explores stopping times, the optional stopping theorem, F-measurable random variables, and martingales.

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

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

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

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

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

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

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

Explores human travel scaling laws, bank note dispersal, random walks, Levy flights, and laser cooling applications.

Covers Levy flights, Central Limit Theorem, and Mesoscopic Master Equation with transition rates in an assurance system.

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

Covers the theory of Brownian motion, diffusion, and random walks, with a focus on Einstein's theory for one-dimensional motion.

Explores martingales, adaptability, and stopping times in stochastic processes.

Explores self-financing strategies, asset pricing theorems, and arbitrage opportunities in financial markets.

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

Covers the concept of Doob's martingale and its properties, including integrability and convergence theorem.