Efficient Steady-state Simulation of High-dimensional Stochastic Networks

Jose Blanchet; Xinyun Chen; Peter Glynn; Nian Si

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arXiv · 2001.08384

Efficient Steady-state Simulation of High-dimensional Stochastic Networks

Jose Blanchet·Xinyun Chen·Peter Glynn·Nian Si

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Abstract

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.

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Jose Blanchet, Xinyun Chen, Peter Glynn, Nian Si. 2020-01-23. Efficient Steady-state Simulation of High-dimensional Stochastic Networks. https://arxiv.org/abs/2001.08384

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