Analysis and use of stochastic models represented by a discrete-time Markov Chain require evaluation of performance measures and characterization of its stationary distribution. Analytical solutions are often unavailable when the system states are continuous or mixed. This paper presents a new method for computing the stationary distribution and performance measures for stochastic systems represented by continuous-, or mixed-state Markov chains. We show the asymptotic convergence and provide deterministic non-asymptotic error bounds for our method under the supremum norm. Our finite approximation method is near-optimal among all discrete approximate distributions, including empirical distributions obtained from Markov chain Monte Carlo (MCMC). Numerical experiments validate the accuracy and efficiency of our method and show that it significantly outperforms MCMC based approach.
翻译:以离散时间马可夫链为代表的随机模型的分析和使用要求评价性能措施并定性其固定分布。当系统状态连续或混合时,通常无法找到分析解决办法。本文为计算由连续或混合状态马可夫链为代表的随机系统的固定分布和性能衡量标准提供了新方法。我们展示了无症状趋同,并为我们的方法提供了符合上层规范的确定性非随机误差界限。我们有限的近似方法在所有离散分布中接近最佳,包括从马尔科夫链蒙特卡洛(MMCC)获得的经验性分布。数字实验验证了我们方法的准确性和效率,并表明它大大优于以MCMC为基础的方法。