论文标题
马尔可夫链大偏差的图形组合方法
Graph-combinatorial approach for large deviations of Markov chains
论文作者
论文摘要
我们考虑了离散的马尔可夫连锁链并研究了对经验占用度量的大偏差，这对于计算纯添加和跳跃型可观察物的波动很有用。我们为有限的时间矩生成函数提供了精确的表达，该函数在循环和路径贡献中分裂，并通过图形组合方法缩放了对配对经验占用度量的缩放累积生成函数。获得的表达使我们能够对相互作用和熵术语以及Lagrange乘数进行物理解释，并可以作为子领导渐近学的起点。我们说明了该方法用于简单的两国马尔可夫链。
We consider discrete-time Markov chains and study large deviations of the pair empirical occupation measure, which is useful to compute fluctuations of pure-additive and jump-type observables. We provide an exact expression for the finite-time moment generating function, which is split in cycles and paths contributions, and scaled cumulant generating function of the pair empirical occupation measure via a graph-combinatorial approach. The expression obtained allows us to give a physical interpretation of interaction and entropic terms, and of the Lagrange multipliers, and may serve as a starting point for sub-leading asymptotics. We illustrate the use of the method for a simple two-state Markov chain.
