Time Parallel Simulation And Hv-Monotonicity

We show how we can make more efficient the time parallel simulation of monotone systems adapting Nicol's approach. We use the monotonicity of a model related to the initial state of the simulation and we prove an algorithm with fix-up computations which minimises the number of runs before we get a consistent sample-path. We obtain proved upper or lower bounds of the sample path of the simulation and bounds of some estimates as well.