论文标题
高阶稳态扩散近似
High order steady-state diffusion approximations
论文作者
论文摘要
我们得出并分析了马尔可夫链的固定分布的新扩散近似，这些分布基于马尔可夫链生成器的扩展中的第二和高阶项。与过去五十年中广泛使用的扩散近似相比，我们的近似值达到了更高的准确性，同时保留了相似的计算复杂性。为了支持我们的近似值，我们在三个不同模型中提出了理论和数值结果的组合。我们的近似值是通过Stein/Poisson方程递归得出的，并且使用Stein的方法证明了理论结果。
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of accuracy compared to diffusion approximations widely used for the past fifty years, while retaining a similar computational complexity. To support our approximations, we present a combination of theoretical and numerical results across three different models. Our approximations are derived recursively through Stein/Poisson equations, and the theoretical results are proved using Stein's method.
