Stochastic approximations of hybrid systems with continuous flow maps

We consider the behavior of stochastic simulators of non-stochastic hybrid systems. We focus on the case where the simulator uses randomness to approximate a (non-stochastic) flow map. The latter is assumed to be a function that is continuous, or globally Lipschitz, for simplicity. Sufficient conditions guaranteeing that the sample paths of solutions to the simulator converge graphically, almost surely as the step size shrinks to zero, to solutions of a corresponding non-stochastic "average" hybrid system are provided. Probabilistic guarantees of closeness on compact time domains are also provided. Copyright (c) 2024 The Authors.