Sticky Brownian Motion and Its Numerical Solution
Sticky Brownian Motion and Its Numerical Solution
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DOI：
10.1137/19m1268446
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发表时间：
2020-03-01
期刊：
影响因子：
10.2
通讯作者：
Holmes-Cerfon, Miranda C.
中科院分区：
文献类型：
--
作者：
Bou-Rabee, Nawaf;Holmes-Cerfon, Miranda C.
粘性布朗运动是扩散过程的最简单的例子，它可以在区域内部和边界上花费有限的时间。它出现在生物、材料科学和金融等领域的各种应用中。本文从应用数学的角度突出了粘性布朗运动的异常行为，并提供了有效模拟它们的工具。我们证明了当粒子扩散到R+上时，粘性布朗运动自然发生，粒子在原点附近具有较强的短程势能。这是一个精确模拟Niesoecale颗粒的极限，这些颗粒的直径约为100 nm-10微米，构成了许多常见材料的基础。我们引入了一种简单直观的粘性随机游动来模拟粘性布朗运动，这也让我们深入了解了它的不同寻常的性质。在有实际意义的参数范围内，我们证明了这种粘性随机游动比模拟粘性布朗运动的其他方法快两到五个数量级。我们概述了将该方法扩展到模拟多维粘性扩散的可能步骤。
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications in fields such as biology, materials science, and finance. This article spotlights the unusual behavior of sticky Brownian motions from the perspective of applied mathematics, and provides tools to efficiently simulate them. We show that a sticky Brownian motion arises naturally for a particle diffusing on R+ with a strong, short-ranged potential energy near the origin. This is a limit that accurately models niesoecale particles, those with diameters approximate to 100nm-10 mu m, which form the building blocks for many common materials. We introduce a simple and intuitive sticky random walk to simulate sticky Brownian motion, which also gives insight into its unusual properties. in parameter regimes of practical interest, we show that this sticky random walk is two to five orders of magnitude faster than alternative methods to simulate a sticky Brownian motion. We outline possible steps to extend this method toward simulating multidimensional sticky diffusions.