This talk was part of the Thematic Programme on "Large Deviations, Extremes and Anomalous Transport in Non-equilibrium Systems" held at the ESI September 19 to October 14, 2022.
In this talk, I will present recent results on generating constrained stochastic processes. First, I will focus on constrained Brownian motion and discuss ways to generate Brownian bridges, meanders and excursions. I will highlight the notion of effective Langevin dynamics and generalise it to the case of discrete-time processes, including the case of Lévy flights. Then, I will extend these results to the case of a non-Markovian process, namely the run-and-tumble particle (RTP), and show how to generate constrained RTP trajectories using effective tumbling rates. Finally, I will discuss the case of an out-of-equilibrium process, the resetting Brownian bridge, and present a surprising effect induced by the resetting and the bridge condition.
