摘要翻译：
我们开发了基于重要性抽样的有效模拟技术，用于三种常见的罕见事件概率，这些事件概率与具有I.I.D.的随机游动有关。有规律地变化的增量；即，1)大偏差概率，2)水平交叉概率，3)再生周期内的水平交叉概率。基于指数扭转的状态无关方法在轻尾增量中可以有效地估计这些概率，但当增量是重尾增量时，这种方法就不适用了。为了解决后一种情况，在过去的几年里，文献中开发了更复杂和优雅的状态相关高效仿真算法。我们提出，通过适当地将这些稀有事件概率分解为一个主导分量和进一步的残差分量，可以为每个分量设计更简单的状态无关重要抽样算法，从而得到具有期望效率性质的复合无偏估计。当增量具有无限方差时，由于即使是众所周知的零方差测度也具有无限的期望终止时间，因此在估计水平交叉概率时也增加了复杂性。我们调整我们的算法，使这个期望是有限的，而估计器仍然是强有效的。从数值上看，所提出的估计器的性能至少与文献中已有的状态相关估计器一样好，有时甚至明显好于文献中已有的状态相关估计器。
---
英文标题：
《State-independent Importance Sampling for Random Walks with Regularly
  Varying Increments》
---
作者：
Karthyek R. A. Murthy, Sandeep Juneja, Jose Blanchet
---
最新提交年份：
2014
---
分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--

---
英文摘要：
  We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation probabilities, 2) the level crossing probabilities, and 3) the level crossing probabilities within a regenerative cycle. Exponential twisting based state-independent methods, which are effective in efficiently estimating these probabilities for light-tailed increments are not applicable when the increments are heavy-tailed. To address the latter case, more complex and elegant state-dependent efficient simulation algorithms have been developed in the literature over the last few years. We propose that by suitably decomposing these rare event probabilities into a dominant and further residual components, simpler state-independent importance sampling algorithms can be devised for each component resulting in composite unbiased estimators with desirable efficiency properties. When the increments have infinite variance, there is an added complexity in estimating the level crossing probabilities as even the well known zero-variance measures have an infinite expected termination time. We adapt our algorithms so that this expectation is finite while the estimators remain strongly efficient. Numerically, the proposed estimators perform at least as well, and sometimes substantially better than the existing state-dependent estimators in the literature.
---
PDF链接：
https://arxiv.org/pdf/1206.3390