Existence and uniqueness of stationary Levy-driven CARMA processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Brockwell, Peter J.¹  Lindner, Alexander² 

[1] Colorado State Univ, Dept Stat, Ft Collins, CO 80523 USA

[2] Tech Univ Carolo Wilhelmina Braunschweig, Inst Math Stochast, D-38106 Braunschweig, Germany

关键词: Levy process;    CARMA process;    Stochastic differential equation;    State-space representation;    Stationarity;    Causality;   

DOI  :  10.1016/j.spa.2009.01.006

来源: Elsevier

【 摘 要 】

Necessary and Sufficient conditions for the existence of a strictly stationary solution of the equations defining a general Levy-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 Levy process. The results generalize results obtained earlier for second-order processes and for processes defined by the Ornstein-Uhlenbeck equation. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free