Existence and uniqueness of stationary Levy-driven CARMA processes

被引：53

作者：

Brockwell, Peter J. ^{[1
]}

Lindner, Alexander ^{[2
]}

机构：

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

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

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2009年 / 119卷 / 08期

关键词：

Levy process; CARMA process; Stochastic differential equation; State-space representation; Stationarity; Causality; CONTINUOUS-TIME ARMA;

D O I：

10.1016/j.spa.2009.01.006

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

070103 [概率论与数理统计]; 140311 [社会设计与社会创新];

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.

引用

页码：2660 / 2681

页数：22

共 13 条

[1]

[Anonymous], 2006, ALEA-LAT AM J PROBAB

[2]

Bernstein D. S., 2005, MATRIX MATH THEORY F

[3]

Brockwell PJ, 2005, STAT SINICA, V15, P477

[4]

Brockwell PJ, 2001, HANDB STAT, V19, P249, DOI 10.1016/S0169-7161(01)19011-5

[5]

Levy-driven CARMA processes [J].

Brockwell, PJ .

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2001, 53 (01) :113-124

[6]

Brockwell PJ., 1991, TIME SERIES THEORY M

[7]

ON FUNCTIONS OF COMPANION MATRICES [J].

ELLER, J .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 96 :191-210

[8]

Kallenberg O., 2002, Foundations of modern probability

[9]

OPERATOR-SELFDECOMPOSABLE DISTRIBUTIONS AS LIMIT DISTRIBUTIONS OF PROCESSES OF ORNSTEIN-UHLENBECK TYPE [J].

SATO, K ;

YAMAZATO, M .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1984, 17 (01) :73-100

[10]

SATO K., 2013, Cambridge Studies in Advanced Mathematics, V68

← 1 2 →