Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes
Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes
复制标题
规则变化随机游走和复合泊松过程中多次跳跃事件的高效稀有事件模拟
DOI：
10.1287/moor.2018.0950
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
B. Zwart
中科院分区：
文献类型：
--
作者：
Bohan Chen;J. Blanchet;C. Rhee;B. Zwart
我们提出了一类非常有效的罕见事件模拟估计器，用于随机游走和复合泊松过程，在一般大偏差范围内具有规则变化的增量/跳跃大小分布。我们的估计器基于重要性采样策略，该策略取决于最近在 Rhee、Blanchet 和 Zwart（2016）中建立的重尾样本路径大偏差结果。新的估计器易于实现，可用于系统地评估各种具有有限相对误差的罕见事件的概率。它们是“通用的”，因为单一重要性采样方案适用于重尾系统中出现的一类非常普遍的罕见事件。特别是，我们的估计器可以处理由多次大跳转（因此超出了单次大跳转的通常原理）引起的罕见事件以及多维过程，例如排队网络的缓冲区内容过程。我们通过数学金融、精算科学和排队论背景下出现的几个应用来说明我们方法的多功能性。
We propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges on the heavy-tailed sample path large deviations result recently established in Rhee, Blanchet, and Zwart (2016). The new estimators are straightforward to implement and can be used to systematically evaluate the probability of a wide range of rare events with bounded relative error. They are "universal" in the sense that a single importance sampling scheme applies to a very general class of rare events that arise in heavy-tailed systems. In particular, our estimators can deal with rare events that are caused by multiple big jumps (therefore, beyond the usual principle of a single big jump) as well as multidimensional processes such as the buffer content process of a queueing network. We illustrate the versatility of our approach with several applications that arise in the context of mathematical finance, actuarial science, and queueing theory.
关于重尾多服务器队列中的大延迟
影响因子：
1.7
作者：
Foss S
通讯作者：
Foss S
DOI：
10.1007/978-1-4419-9473-8
发表时间：
2011-01-01
期刊：
INTRODUCTION TO HEAVY-TAILED AND SUBEXPONENTIAL DISTRIBUTION
影响因子：
--
作者：
Foss, Sergey;Korshunov, Dmitry;Zachary, Stan
通讯作者：
Zachary, Stan