Sample-path large deviations for a class of heavy-tailed Markov-additive processes
Sample-path large deviations for a class of heavy-tailed Markov-additive processes
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DOI：
10.1214/24-ejp1115
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发表时间：
2020-10
影响因子：
1.4
通讯作者：
Bohan Chen;C. Rhee;B. Zwart
中科院分区：
文献类型：
--
作者：
Bohan Chen;C. Rhee;B. Zwart
对于由仿射递归 $X_{n+1} = A_n X_n + B_n$ 驱动的一类加性过程，我们在 $D [0,1]$ 上的 $M_1'$ 拓扑中开发了样本路径大偏差原理。我们允许 $B_n$ 具有两个符号，并重点关注 Kesten 条件在 $A_1$ 上成立的情况，从而导致重尾分布。我们的大偏差结果中最可能的路径是具有正跳跃和负跳跃的阶跃函数。
For a class of additive processes driven by the affine recursion $X_{n+1} = A_n X_n + B_n$, we develop a sample-path large deviations principle in the $M_1'$ topology on $D [0,1]$. We allow $B_n$ to have both signs and focus on the case where Kesten's condition holds on $A_1$, leading to heavy-tailed distributions. The most likely paths in our large deviations results are step functions with both positive and negative jumps.