Transition Law-based Simulation of Generalized Inverse Gaussian Ornstein–Uhlenbeck Processes
Transition Law-based Simulation of Generalized Inverse Gaussian Ornstein–Uhlenbeck Processes
复制标题
DOI：
10.1007/s11009-010-9179-6
复制
发表时间：
2011-09
影响因子：
0.9
通讯作者：
Shibin Zhang
中科院分区：
文献类型：
--
作者：
Shibin Zhang
本文将Ornstein-Uhlenbeck型随机积分表示为三个独立的随机变量之和，其中一个随机变量的密度是两个广义逆高斯分布的密度的反卷积，另两个随机变量的密度都是复合Poisson分布.基于随机积分的表示，给出了一种求解给定广义逆高斯分布的Ornstein-Uhlenbeck过程离散观测值的模拟方法.对于广义逆高斯Ornstein-Uhlenbeck过程的某些子类，新息可以精确采样。一些实证结果证明了模拟方法的性能。
In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of three independent random variables—one follows a distribution whose density is a deconvolution of the densities of two generalized inverse Gaussian distributions, and the two others all have compound Poisson distributions. Based on the representation of the stochastic integral, a simulation procedure for obtaining discretely observed values of Ornstein–Uhlenbeck processes with given generalized inverse Gaussian distribution is provided. For some subclasses of the generalized inverse Gaussian Ornstein–Uhlenbeck process, the innovations can be sampled exactly. The performance of the simulation method is evidenced by some empirical results.