Martingale Difference

Martingale difference sequences, essentially sequences of random variables where the expected value of each term, given the past, is zero, are a fundamental tool in probability theory and statistics. Current research focuses on applying this concept to diverse areas, including sequential hypothesis testing (e.g., using kernelized Stein discrepancies and e-processes), diagnosing distribution shifts in machine learning systems, and analyzing the behavior of reinforcement learning algorithms (e.g., q-learning under Tsallis entropy). This versatile framework enables rigorous analysis of stochastic processes and provides powerful tools for developing statistically sound and computationally efficient algorithms across various fields, from financial modeling to system identification.