Generalized Skorokhod's Reflecting Problem - Lecture 1

Explore a comprehensive lecture from Professor Andrey Pilipenko of the National Academy of Sciences of Ukraine, delivered as part of the Stochastic Systems for Anomalous Diffusion program. Delve into the mathematical foundations of Skorokhod's reflection, first introduced in 1961 for creating reflected diffusion on the half-line, and its evolution to handle processes with jumps like reflected Lévy processes. Learn how reflected processes on the half-line function as weak limits of random walks with switching regimes at zero, examining both the behavior away from and around zero. Master the general theory of regime changes and understand the convergence to functions with generalized reflection through deterministic results applicable to various stochastic processes. Discover practical applications including storage processes, heavy traffic limits, and diffusion on a half-line featuring continuous reflection, jump exit, and delay at zero.