Lectures related to Linear Response and Complex Diffusivity

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.

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.

Stochastic Integration: First Steps

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

Stochastic Calculus: Itô's Formula

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

Martingale-based Methods for Stochastic Systems

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

Sub- and Supermartingales: Theory and Applications

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

Stochastic Calculus: Interest Rate Models

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

Martingales and Stochastic Integration

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

Quantum and Nanocomputing

Explores conduction in quantum dot and discrete energy levels for nanocomputing.

Martingales and Brownian Motion

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

Stochastic Calculus: Integrals and Processes

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

Analytical Geometry: Bisectors and Areas

Explores the properties of bisectors and areas in Analytical Geometry.

Designing Spaces: Movement and Architecture

Explores the relationship between movement and architecture, focusing on the collaboration between choreographers and designers.

Optimization Algorithms

Covers optimization algorithms, convergence properties, and time complexity of sequences and functions.

Probability Distributions in Environmental Studies

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

Expander Graphs: Properties and Eigenvalues

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Stochastic Differential Equations

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

Stochastic Calculus: Brownian Motion

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

Martingales and Brownian Motion Construction

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