Lectures related to Martingale (probability theory)

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

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.

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.

Generalization of Martingales: Sub- & Supermartingales

Explores the generalization of martingales to sub- and supermartingales with a focus on convergence properties.

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.

Martingale Convergence

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

Martingale Convergence Theorem: Version 1

Introduces the martingale convergence theorem and demonstrates its application with examples.

Martingale Convergence Theorem

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

Generalizations to Sub- & Supermartingales

Covers the generalizations of sub- & supermartingales and the existence of random variables.

Optional Stopping Theorem

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

Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Martingale Convergence Theorem

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

Reflection Principle: Proof and Observations

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

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.

Asset Pricing: Fundamental Theorems

Covers the fundamental theorems of asset pricing, including EMM, self-financing strategies, risk-neutral pricing, and completeness of markets.

Linear Response and Complex Diffusivity

Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.

Martingales: Definitions and Theorems

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

Stopping Times: Martingales and Brownian Motion

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