论文标题
扩散第一次退出时间的精确模拟：算法加速度
Exact simulation of diffusion first exit times: algorithm acceleration
论文作者
论文摘要
为了描述或估计与特定随机变量相关的不同数量，数值生成这种变体是主要的关注。在特定情况下，随机变量的确切产生可能是瞬时无法使用的，或者在计算时间方面太昂贵。因此，它需要用近似程序代替。与以前的情况一样，扩散过程的退出时间的雄心勃勃的精确模拟涉及数学金融，神经科学或可靠性等不同领域的许多应用。描述退出时间的通常方法是使用离散化方案，这当然是近似程序。最近，Herrmann和Zucca \ cite {Herrmann-Zucca-2}提出了一种新算法，即所谓的GDET-Algorithm（一般扩散出口时间），该算法允许在一维扩散中模拟出口时间。使用接受性拒绝抽样的精确仿真方法的唯一缺点是它们的时间消耗。在本文中，作者强调了基于多臂强盗模型的GDET-Algorithm的加速过程。通过数值示例指出了这种加速度的效率。
In order to describe or estimate different quantities related to a specific random variable, it is of prime interest to numerically generate such a variate. In specific situations, the exact generation of random variables might be either momentarily unavailable or too expensive in terms of computation time. It therefore needs to be replaced by an approximation procedure. As was previously the case, the ambitious exact simulation of exit times for diffusion processes was unreachable though it concerns many applications in different fields like mathematical finance, neuroscience or reliability. The usual way to describe exit times was to use discretization schemes, that are of course approximation procedures. Recently, Herrmann and Zucca \cite{Herrmann-Zucca-2} proposed a new algorithm, the so-called GDET-algorithm (General Diffusion Exit Time), which permits to simulate exactly the exit time for one-dimensional diffusions. The only drawback of exact simulation methods using an acceptance-rejection sampling is their time consumption. In this paper the authors highlight an acceleration procedure for the GDET-algorithm based on a multi-armed bandit model. The efficiency of this acceleration is pointed out through numerical examples.
