Sub- and Supermartingales: Theory and Applications

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 2 of 4

Optional Stopping Theorem: Proof and Applications

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

Martingale Convergence

Explores martingale convergence, discussing the conditions for convergence and variance in martingales.

Doob's Martingale

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

Martingale Convergence Theorem

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

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.

Optional Stopping Theorem: Martingales and Stepping Times

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

Martingales and Brownian Motion Construction

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

Martingales and Brownian Motion

Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.

Fourier Transform and Spectral Densities

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