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Extension of Stationary Stochastic Processes
K. R. Parthasarathya,
S. R. S. Varadhanb a Indian Statistical Institute, Calcutta
b Indian Statistical Institute, Calcutta
Abstract:
A process
$\xi _\lambda (t)$ of the form (2) is observed, where
$S(t-\tau )$ is a signal of a well-known form, which depends on an unknown parameter
$\tau$;
$\nu(t)$ is Gaussian noise with a spectral density as in (la). The problem is to detect a class of estimations of the parameter
$\tau$, whose exactness does not vary when the process
$\xi _\lambda (t)$ changes somewhat. A class of processes
$\tilde{\xi}_\lambda (t)$ approximating the process
$\xi _\lambda(t)$ is determined by means of relation (3). A class of estimations
$\tilde\tau$, whose exactness is the same for all processes
$\tilde\xi _\lambda$ approximating the process
$\xi _\lambda$, is determined from (4). An optimum estimation for this class is found.
Received: 10.12.1962
Language: English