Lectures related to Stochastic Integration

Stochastic Integral: Isometry Continuity

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Quadratic Variation: Martingales and Stochastic Integrals

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

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Stochastic Calculus: Integrals and Processes

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

Stochastic Calculus: Brownian Motion

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

Stochastic Differential Equations

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

Stochastic Calculus: Interest Rate Models

Provides an overview of stochastic calculus and its applications in interest rate models and financial modeling.

Stochastic Calculus: Foundations and Applications

Explores the foundation of stochastic calculus, emphasizing deterministic and memoryless processes.

Turbulent State Symmetries

Explores broken and emerging symmetries in turbulent states, discussing energy cascades, lack of scale invariance, and potential conformal invariance.

Fourier Transform and Spectral Densities

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

Stochastic Integration: First Steps

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

Stochastic Calculus: Lecture 1

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.

Martingales and Brownian Motion Construction

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

Martingales and Stochastic Integration

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

Asset Pricing Theory: Dynamic Arbitrage Pricing

Covers the first theorem of asset pricing, self-financing portfolios, replication, Kolmogorov equations, and pricing strategies.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Interest Rate Models: Introduction

Covers the fundamentals of interest rates and stochastic models in finance.

Martingale-based Methods for Stochastic Systems

Explores martingales in stochastic systems, focusing on formal analysis, termination analysis, and stability verification.

Spatial Ergodicity for SPDEs

Explores spatial ergodicity for SPDEs, covering basic formulations, initial data effects, and results on ergodicity and CLT.

Sub- and Supermartingales: Theory and Applications

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