关于（跳跃）扩散的精确和$\varepsilon$ -强模拟
On the exact and $\varepsilon$-strong simulation of (jump) diffusions
摘要：
本文介绍了一个框架，用于模拟有限维表示（跳跃）扩散样本路径在有限的时间间隔，没有离散化误差（确切地），在这样一种方式，可以恢复在任何有限的时间点的样本路径。在这个框架内，我们扩展现有的精确算法，并引入新的自适应方法。我们认为，在本文中开发的方法，它允许模拟的上限和下限的过程，几乎肯定限制（跳）扩散样本路径到任何指定的公差的应用。我们证明了我们的方法的有效性，通过有限的计算，它是可能的，以确定样本路径是否跨越各种不规则的障碍，模拟到任何指定的公差的第一次击中时间的不规则的障碍和模拟杀死扩散样本路径。
英文摘要：
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any finite collection of time points. Within this framework we extend existing exact algorithms and introduce novel adaptive approaches. We consider an application of the methodology developed within this paper which allows the simulation of upper and lower bounding processes which almost surely constrain (jump) diffusion sample paths to any specified tolerance. We demonstrate the efficacy of our approach by showing that with finite computation it is possible to determine whether or not sample paths cross various irregular barriers, simulate to any specified tolerance the first hitting time of the irregular barrier and simulate killed diffusion sample paths.
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