Lectures related to Martingale-based Methods for Stochastic Systems

Martingales and Brownian Motion Construction

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

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

Neuromorphic Computing: Concepts and Hardware Implementations

Covers neuromorphic computing, challenges in ternary and binary computing, hardware simulations of the brain, and new materials for artificial brain cells.

Diffusion Models in Generative Modeling

Explores diffusion models in generative modeling, covering probability estimation, data generation, and model evaluation.

State Space Models: Expressivity of Transformers

Covers state space models and the expressivity of transformers in sequence copying tasks.

Stochastic Integral: Isometry Continuity

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

Generalization of Martingales

Explores the generalization of Martingale Central Limit Theorem to sub- and supermartingales, discussing key properties and corollaries.

Fokker-Planck & KPZ Equations

Explores the Fokker-Planck and KPZ equations in stochastic processes and random growth models.

Stochastic Models for Communications: Discrete-Time Markov Chains - Absorption Time

Discusses discrete-time Markov chains and absorption time in communication systems.

Quadratic Variation: Martingales and Stochastic Integrals

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

Score-based Generative Modelling

Explores score-based generative modelling through stochastic differential equations, emphasizing denoising score matching and diffusion probabilistic models.

Linear Response and Complex Diffusivity

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

Quantum Decision-Making: Neural Network Privacy

Covers the quantum decision-making model and its implications for neural network privacy and image recognition.

Martingales and Brownian Motion

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

Stochastic Calculus: Itô's Formula

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

Stochastic Integration: First Steps

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

The Marriage Problem

Explores the marriage problem, modeling the process as a controlled stochastic process with dynamic programming algorithms to find the optimal policy for accepting bachelors.

Stochastic Processes: Symmetric Random Walk

Covers the properties of the symmetric random walk in stochastic processes.

Stochastic Models for Communications: Continuous-Time Stochastic Processes

Covers examples of continuous-time stochastic processes in communications.

Martingales and Stochastic Integration

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