Existence and uniqueness of stationary Lvy-driven CARMA processes
Existence and uniqueness of stationary Lvy-driven CARMA processes
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固定 Lvy 驱动的 CARMA 过程的存在性和唯一性
DOI：
10.1016/j.spa.2009.01.006
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Alexander M. Lindnery
中科院分区：
文献类型：
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作者：
P. Brockwell;Alexander M. Lindnery
给出了一类广义Lévy驱动的指标集为R的连续参数ARMA过程方程存在严格平稳解的充要条件.在此条件下，证明了解是唯一的，并给出了该过程关于驱动Lévy过程的背景积分的显式表达式。这些结果推广了先前关于二阶过程和由Ornstein-Uhlenbeck方程定义的过程的结果。
Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining a general Lévy-driven continuous-parameter ARMA process with index set R are determined. Under these conditions the solution is shown to be unique and an explicit expression is given for the process as an integral with respect to the background driving Lévy process. The results generalize results obtained earlier for second-order processes and for processes defined by the Ornstein–Uhlenbeck equation.