Stochastic Level-crossing Estimation of Stationary Probability Distributions in Stochastic Models
Percy H. Brill, Mei Ling Huang · Zenodo (CERN European Organization for Nuclear Research) · 2023
This paper discusses a Monte Carlo simulation technique, Level Crossing Estimation (LCE) for computing the stationary probability distribution of a key random variable in a stochastic model. We first sketch a typical sample path of the key random variable over time. Simple previously proved theorems show that the sample-path down-crossing rate of an arbitrary fixed state-space level is equal to a simple mathematical function of the analytic stationary probability density function (p.d.f.) of the random variable. This leads to construction of a step function over a state-space partition, which is an estimate of the true stationary p.d.f.. The finer the partition, the closer is the estimate. We illustrate the technique using an example of estimating the stationary p.d.f. of the virtual wait in a variate of an M/M/1 queue.