论文标题
泊松方程的解决方案随机单调马尔可夫链
Solutions of Poisson's Equation for Stochastically Monotone Markov Chains
论文作者
论文摘要
随机单调马尔可夫链在许多应用域中出现，尤其是在队列和存储系统的环境中。 Poisson的方程是分析此类模型的加性功能的关键工具，例如等待时间的累积总和或奖励总和。在本文中，我们表明，当这种马尔可夫链的奖励函数是单调时，泊松方程的解决方案是单调的。这意味着，当奖励是单调时，与无限地平线平均奖励相关的价值函数是单调的。
Stochastically monotone Markov chains arise in many applied domains, especially in the setting of queues and storage systems. Poisson's equation is a key tool for analyzing additive functionals of such models, such as cumulative sums of waiting times or sums of rewards. In this paper, we show that when the reward function for such a Markov chain is monotone, the solution of Poisson's equation is monotone. This implies that the value function associated with infinite horizon average reward is monotone in the state when the reward is monotone.
