Lectures related to Quadratic variation

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.

Quadratic Variation: Martingales and Stochastic Integrals

Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.

Joint Quadratic Processes

Covers the concept of joint quadratic processes and their properties.

Martingale Convergence

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

Semimartingale: Joint Variation Process

Covers semimartingales, Ito's lemma, and polynomial demonstrations, emphasizing the management of second-order terms and induction reasoning.

Stochastic Calculus: Brownian Motion

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Stochastic Calculus: Integrals and Processes

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.

Martingale Convergence Theorem

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

Doob's Decomposition Theorem

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

Sub- and Supermartingales: Theory and Applications

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

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.

Stochastic Integration: First Steps

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

Martingale Convergence Theorem

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

Girsanov: Martingales and Brownian Motion

Explores martingales, Brownian motion, and measure transformations in probability theory.

Martingales and Stochastic Integration

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

Parameter Estimation of SDEs with Linear Response Theory

Explores parameter estimation of SDEs using Linear Response Theory and covers challenges, examples, algorithms, and convergence.

Martingale Convergence Theorem: Version 1

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

OTA: Slew Rate, Signal Integrity and Offset

Explores large signal bandwidth, slew rate, signal integrity, offset, dynamic range, and power supply rejection ratio in operational amplifiers.

Doob's Martingale

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

Advanced Analysis II: Variation of Constants Method

Covers the variation of constants method for solving first-order linear differential equations, detailing its steps and implications for general and particular solutions.