论文标题
高维随机网络的有效稳态模拟
Efficient Steady-state Simulation of High-dimensional Stochastic Networks
论文作者
论文摘要
我们提出并研究了渐近最佳的蒙特卡洛估计量，以对D维反射的布朗运动的稳态预期。从某种意义上说，我们的估计器在$ \ tilde {o}（d）$（$ d $中的对数因素上）I.I.D。的渐近上是最佳的。高斯随机变量以输出具有控制误差的估计值。我们的构建基于对合适的多层次蒙特卡洛策略的分析，我们认为，该策略可以广泛应用。这是第一种具有线性复杂性（在适当的规律性条件下）的算法，随着尺寸的增加，RBM的稳态估计。
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 $\tilde{O}(d)$ (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.
