A large deviations perspective on the efficiency of multilevel splitting
A large deviations perspective on the efficiency of multilevel splitting
复制标题
多级分裂效率的大偏差视角
DOI：
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发表时间：
1998
影响因子：
6.8
通讯作者：
T. Zajic
中科院分区：
文献类型：
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作者：
P. Glasserman;P. Heidelberger;P. Shahabuddin;T. Zajic
我们分析了一个最近提出的电信文献中的罕见事件模拟的多级分裂方法的性能。该方法将有希望的路径分成中间水平的子路径，以增加罕见事件的观测数量。在我们的前一篇文章（1997）中，我们给出了在特定类型的模型中，这种方法是渐近最优的充分条件;这里我们关注的是在一般情况下的必要条件。我们显示，通过各种各样的结果，选择中间阈值的重要性的方式一致的最有可能的路径到一个罕见的集，无论是当水平的数量是固定的，当它增加的事件的稀有性。在后一种情况下，我们给出了非常一般的必要条件的基础上大偏差率函数。这表明，即使适当地选择了中间水平，该方法也常常不能达到渐近最优。我们用例子来说明这些条件。
We analyze the performance of a multilevel splitting method for rare event simulation related to one recently proposed in the telecommunications literature. This method splits promising paths into subpaths at intermediate levels to increase the number of observations of a rare event. In our previous paper (1997) we gave sufficient conditions, in specific classes of models, for this method to be asymptotically optimal; here we focus on necessary conditions in a general setting. We show, through a variety of results, the importance of choosing the intermediate thresholds in a way consistent with the most likely path to a rare set, both when the number of levels is fixed and when it increases with the rarity of the event. In the latter case, we give very general necessary conditions based on large deviations rate functions. These indicate that even when the intermediate levels are chosen appropriately, the method will frequently fail to be asymptotically optimal. We illustrate the conditions with examples.