Martingale-based Methods for Stochastic Systems

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Sub- and Supermartingales: Theory and Applications

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

Random Walks: Return Probabilities in Multiple Dimensions

Covers the analysis of random walks and their return probabilities in multiple dimensions.

Stochastic Reaction Simulation: Constantin

Covers the algorithm to simulate molecule reactions using random numbers.

Stochastic Calculus: Brownian Motion

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

Probability and Stochastic Processes: Fundamentals and Applications

Discusses the fundamentals of probability and stochastic processes, focusing on random variables, their properties, and applications in statistical signal processing.

Probability Distributions in Environmental Studies

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

Markov Chains: Theory and Applications

Covers the theory and applications of Markov chains in modeling random phenomena and decision-making under uncertainty.

Probabilistic Functions: Free Fields and Random Variables

Covers free fields and probabilistic functions, focusing on random variables and their properties.

Diffusion Models and Robustness

Explores diffusion models, GAN training challenges, SDE-based generative models, and robustness in deep learning.

Adaptive Signal Processing: Filtering & Neural Networks

Explores adaptive signal processing, gradient descent, and the LMS algorithm for efficient filtering and neural network training.