论文标题
由$α$稳定噪声驱动的非lipschitz随机微分方程的模拟：基于确定性均质化的方法
Simulation of non-Lipschitz stochastic differential equations driven by $α$-stable noise: a method based on deterministic homogenisation
论文作者
论文摘要
我们设计了一种明确的方法，将$α$稳定的随机微分方程（SDE）与非lipschitz系数集成在一起。为了减轻由Lévy噪声的无限增量引起的数值不稳定性，我们使用确定性映射，该图具有所需的SDE作为其同质极限。此外，我们的方法自然克服了明确表达Marcus积分的困难。我们提出了一个具有自然边界的SDE的示例，表明我们的方法尊重边界，而欧拉山的离散化则无法做到这一点。作为副产品，我们设计了一种完全确定性的方法来构建$α$稳定的法律。
We devise an explicit method to integrate $α$-stable stochastic differential equations (SDEs) with non-Lipschitz coefficients. To mitigate against numerical instabilities caused by unbounded increments of the Lévy noise, we use a deterministic map which has the desired SDE as its homogenised limit. Moreover, our method naturally overcomes difficulties in expressing the Marcus integral explicitly. We present an example of an SDE with a natural boundary showing that our method respects the boundary whereas Euler-Maruyama discretisation fails to do so. As a by-product we devise an entirely deterministic method to construct $α$-stable laws.
