Lectures related to Stochastic Calculus: Brownian Motion

Stochastic Calculus: Itô's Formula

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.

Quadratic Variation: Martingales and Stochastic Integrals

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

Stochastic Calculus: Interest Rate Models

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

Martingales and Brownian Motion Construction

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

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 Differential Equations

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

Stochastic Integral: Isometry Continuity

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

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Stochastic Calculus: Lecture 1

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

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.

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.

Probability Distributions in Environmental Studies

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

Joint Quadratic Processes

Covers the concept of joint quadratic processes and their properties.

Martingales and Brownian Motion

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

Martingales and Stochastic Integration

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

Stochastic Calculus: Foundations and Applications

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

Girsanov: Martingales and Brownian Motion

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