On the representation of nonlinear systems with gaussian inputst†
- 1 January 1979
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 2 (1-4) , 173-189
- https://doi.org/10.1080/17442507908833124
Abstract
An arbitrary nonlinear system with input a Gaussian process, which is such that its output process has finite second moments, admits two kinds of representations: the first in terms of a sequence of deterministic kernels and the second in terms of a single stochastic kernel. We consider here the identification of the sequence of deterministic kernels from the input and output processes, the representation of the system output when its input is a sample function of the Gaussian process or another equivalent Gaussian process, and the relationship of the sequence of kernels mentioned above to the Volterra expansion kernels when the system has a Volterra representation.Keywords
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