CARMA(p,q) generalized random processes

被引：10

作者：

Brockwell, Peter J. ^{[1
]}

Hannig, Jan ^{[2
]}

机构：

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

[2] Univ N Carolina, Chapel Hill, NC USA

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2010年 / 140卷 / 12期

基金：

美国国家科学基金会;

关键词：

Generalized random process; CARMA process; White noise; Stochastic differential equation; State-space representation;

D O I：

10.1016/j.jspi.2010.04.028

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：

There is now a vast literature on the theory and applications of generalized random processes, pioneered by Ito (1953), Gel'fand (1955) and Yaglom (1957). In this note we make use of the theory of generalized random processes as defined in the book of Gel'fand and Vilenkin (1964) to extend the definition of continuous-time ARMA(p,q) processes to allow q >= p, in which case the processes do not exist in the classical sense. The resulting CARMA generalized random processes provide a framework within which it is possible to study derivatives of CARMA processes of arbitrarily high order. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：3613 / 3618

页数：6

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