论文标题
样品路径大偏差，用于反射的随机步行的无限添加功能
Sample-path large deviations for unbounded additive functionals of the reflected random walk
论文作者
论文摘要
我们证明了一个样品路径大偏差原理（LDP），具有子线性速度，用于林德利递归引起的某些马尔可夫链的无界功能。 LDP保留在Skorokhod空间$ \ mathbb {d} [0，t] $配备了$ M_1' $拓扑。我们的技术取决于马尔可夫链的合适分解，以再生周期为单位。每个再生周期表示在反射随机行走的繁忙时期内积累的面积。在MRW的繁忙时期，我们证明了该地区的一个巨大偏差原则，我们表明它表现出了重型的行为。
We prove a sample path large deviation principle (LDP) with sub-linear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space $\mathbb{D}[0,T]$ equipped with the $M_1'$ topology. Our technique hinges on a suitable decomposition of the Markov chain in terms of regeneration cycles. Each regeneration cycle denotes the area accumulated during the busy period of the reflected random walk. We prove a large deviation principle for the area under the busy period of the MRW, and we show that it exhibits a heavy-tailed behavior.
