Editorial foreword to special issue on Simulation of Stochastic Networks and related topics

Abstract

This special issue contains a selection of papers which are based on some of the invited lectures that were given at the workshop on Simulation of Stochastic Networks which took place on June 21–23, 2010 at the Newton Institute of Mathematical Sciences in Cambridge, UK. The workshop, which was dedicated to topics related to estimation of rare events as well as other aspects including simulation of stochastic differential equations (SDEs), and steady-state simulation, was attended by over fifty active researchers and leading experts in the fields of applied probability and stochastic simulation. The special issue cuts across different areas at the intersection of applied probability and stochastic simulation and we believe that an important strength of the issue is that the contributions suggest interesting research avenues in their respective areas. We therefore hope that the readers will enjoy these contributions and feel enticed to venture into the topics that concern the papers in this special issue. The first paper in this special issue, Analysis of an interacting particle method for rare event estimation, is authored by Yi Cai and Paul Dupuis. The paper studies a class of interacting particle systems for Monte Carlo estimation of large deviations probabilities based on finding a subsolution to a certain partial differential equation (PDE). In recent years, the subsolution approach has become one of the standard methods for constructing rare event simulation estimators with suitable optimality properties. The authors extend, at least in the context of onedimensional problems, the subsolution approach for constructing suitable optimal estimators to a much broader class of particle methods. Surprisingly, they show that the PDE associated to interacting particle