Persistence Probabilities for Random Walks and Related Processes

Explore persistence probabilities for random walks, autoregressive sequences, and moving average sequences in this 48-minute mathematical lecture. Delve into the generating functions of these random processes to uncover their fundamental properties and behavior patterns. Discover the fascinating connections between persistence probabilities and special mathematical functions, including deformed exponential functions and generating functions of combinatorial polynomials. Learn how these theoretical concepts apply across different types of stochastic processes and gain insights into the mathematical frameworks used to analyze their long-term behavior. The presentation provides a rigorous examination of probability theory and its applications to understanding the persistence characteristics of various random mathematical models.