Efficient Steady-state Simulation of High-dimensional Stochastic NetworksJose Blanchet, Xinyun Chen, Peter W. Glynn, and Nian Si Stochastic Systems, Volume 11, Number 2 (2021). We propose and study an asymptotically optimal Monte Carlo estimator for steady-state expectations of a d-dimensional reflected Brownian motion. Our estimator is asymptotically optimal in the sense that it requires Õ (d) (up to logarithmic factors in d) i.i.d. Gaussian random variables in order to output an estimate with a controlled error. Our construction is based on the analysis of a suitable multi-level Monte Carlo strategy which, we believe, can be applied widely. This is the first algorithm with linear complexity (under suitable regularity conditions) for steady-state estimation of RBM as the dimension increases. |