Martingale-based Methods for Stochastic Systems

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Martingales and Brownian Motion Construction

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

Stochastic Calculus: Lecture 1

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.