Characterizing innovations realizations for random processes
作者:
Carla A. Schwartzt,
Bradley W. Dickinsont,
Eduardo D. Sontagt,
期刊:
Stochastics
(Taylor Available online 1984)
卷期:
Volume 11,
issue 3-4
页码: 159-172
ISSN:0090-9491
年代: 1984
DOI:10.1080/17442508308833283
出版商: Gordon and Breach Science Publishers Inc
数据来源: Taylor
摘要:
In this paper we are concerned with the theory of second order (linear) innovations for discrete random processes. We show that of existence of a finite dimensional linear filter realizing the mapping from a discrete random processto innovations is equivalent to a certain semiseparable structure of the covariance sequence of the process. We also show that existence of a finite dimensional realization (linear or nonlinear) of the mapping from a process to its innovations implies that the process have this semiseparable covariance sequence property. In particular, for a stationary random process, the spectral density function must be rational.
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