Martingale-based Methods for Stochastic Systems

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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.