Rate-tilting for fast simulation of level/phase processes
Efficient simulation methods for stochastic processes involving rarely occurring events is in the center of this work. The process considered is the so-called level/phase process, a Markov process in which the ``level'' and the ``phase'' are two state variables. Changes of ``level'' and ``phase'' are induced by events, which have rates that are independent of the level except at a ``boundary''. If a system typically stays at lower levels, then reaching a high level \(n\) is a rare event, thus direct simulation is very inefficient. The authors suggest to change the events rates in a level/phase process to accelerate simulation, and find the so-called hitting probability entering a rare event by simulation. This method is called ``rate-tilting''. A proper construction of ``rate-tilting'' relates to a generalized eigenvalue problem involving the infinitesimal generator matrix \(Q\) of the process being considered. It is shown that the relative estimation error of the hitting probability resulting from the proposed simulation remains bounded as the level increases, provided that the boundary set of the state space satisfies certain conditions. They provide criteria when ``rate-tilting'' is advantageous. However, it may be noted that ``rate-tilting'' is not always increasing the efficiency of simulations.
scientific article; zbMATH DE number 2081266