论文标题
$ p $ tempered $α$稳定的OU流程的有效仿真
Efficient Simulation of $p$-Tempered $α$-Stable OU Processes
论文作者
论文摘要
我们开发有效的方法来模拟与$ p $ tempered $α$ stable（$ \ ts $）分布相关的Ornstein-Uhlenbeck类型的过程。我们的结果均适用于单变量和多元案例，我们认为$ \ ts $分布是固定法律，并且是背景驾驶LévyProcess（BDLP）的分布。在后一种情况下，我们还得出了过渡法的明确表示，因为这仅在某些特殊情况下才知道，仅在$ p = 1 $和$α\ [0,1）$中才知道。仿真结果表明我们的方法在实践中效果很好。
We develop efficient methods for simulating processes of Ornstein-Uhlenbeck type related to the class of $p$-tempered $α$-stable ($\ts$) distributions. Our results hold for both the univariate and multivariate cases and we consider both the case where the $\ts$ distribution is the stationary law and where it is the distribution of the background driving Lévy process (BDLP). In the latter case, we also derive an explicit representation for the transition law as this was previous known only in certain special cases and only for $p=1$ and $α\in[0,1)$. Simulation results suggest that our methods work well in practice.
