Title: Stochastic Path Integrals and Large Deviations

Abstract: In this talk, I will first recap the theory of path integral representations for classical stochastic processes, with a focus on examples like Langevin dynamics. Building on this, I will present recent results (arXiv:2411.00490) on extending these concepts to quantum stochastic processes through stochastic Schrödinger equations. Additionally, I will introduce Metropolis Monte Carlo schemes, such as transition path sampling, which are effective for sampling rare events from path ensembles when brute-force sampling is infeasible due to the rarity of these events.