Simulation of Stochastic Volterra Equations Driven by Space–Time Lévy Noise
Simulation of Stochastic Volterra Equations Driven by Space–Time Lévy Noise
复制标题
时空 Lévy 噪声驱动的随机 Volterra 方程模拟
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
C. Kluppelberg
中科院分区：
文献类型：
--
作者：
Bohan Chen;Carsten Chong;C. Kluppelberg
本文研究了模拟纯跳跃型时空Levy噪声驱动的随机Volterra方程的两种数值格式。第一种方法基于截断噪声的小跳跃，第二种方法依赖于无穷可分随机变量的级数表示技术。在合理的假设下，我们证明了这两种方法(L^p)的逼近都收敛于Volterra方程的真解。我们给出了关于Volterra核和噪声特征的显式收敛速度。模拟研究可视化了所研究过程的最重要的路径属性。
In this paper we investigate two numerical schemes for the simulation of stochastic Volterra equations driven by space–time Levy noise of pure-jump type. The first one is based on truncating the small jumps of the noise, while the second one relies on series representation techniques for infinitely divisible random variables. Under reasonable assumptions, we prove for both methods (L^p)- and almost sure convergence of the approximations to the true solution of the Volterra equation. We give explicit convergence rates in terms of the Volterra kernel and the characteristics of the noise. A simulation study visualizes the most important path properties of the investigated processes.