Lectures related to Martingale Convergence Theorem: Proof and Stopping Time

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.

Martingale Convergence Theorem

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

Optional Stopping Theorem: Proof and Applications

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

Sub- and Supermartingales: Theory and Applications

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

Optional Stopping Theorem: Martingales and Stepping Times

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

Fourier Inversion Formula

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Martingale Convergence Theorems

Explores the convergence of martingales under specific conditions and previews upcoming topics on martingale theorems and inequalities.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Doob's Decomposition Theorem

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

Martingale Convergence

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

Martingale Convergence Theorem

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

Doob's Martingale

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

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Inductive Propositions: Reasoning and Evaluation Techniques

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

The Languages of Isabelle: Isar, ML, and Scala

Explores the languages of Isabelle, focusing on Isar, ML, and Scala, covering proof schemes, Natural Deduction rules, inductive definitions, and the LCF approach.

Stopping Times: Martingales and Brownian Motion

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

Martingales and Stochastic Integration

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

Probability Convergence

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Martingales and Brownian Motion: Three Stopping Theorems

Explores three stopping theorems in martingales and Brownian motion.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.