Constrained Stochastic Processes: From Brownian Motion to Run-and-Tumble Particles

Explore recent findings on generating constrained stochastic processes in this 32-minute conference talk from the Thematic Programme on "Large Deviations, Extremes and Anomalous Transport in Non-equilibrium Systems" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into constrained Brownian motion, examining methods for generating Brownian bridges, meanders, and excursions. Discover the concept of effective Langevin dynamics and its extension to discrete-time processes, including Lévy flights. Investigate the application of these results to non-Markovian processes, specifically the run-and-tumble particle (RTP), and learn how to generate constrained RTP trajectories using effective tumbling rates. Conclude by examining an out-of-equilibrium process, the resetting Brownian bridge, and uncover a surprising effect caused by the interplay of resetting and bridge conditions.