Improving Time Parallel Simulation for Monotone Systems

We improve the efficiency of time parallel simulation using some concepts of monotonicity of simulation models. The time parallel simulation technique partitions the simulation timespan into simulation periods which are independently executed. Such a technique relies on strong stochastic assumptions: regeneration or short influence of the initial point a on sample path. If these assumptions are not satisfied, we only obtain an approximation. We prove that if the model is monotone we can increase the parallelization of the simulations and we can prove some bounds on the result.