A minimax test for hypotheses on a spectral density

Assume that on the set of the values t = 1, , k there is given a realization of the Gaussian stationary process X_t with spectral density f(), (0, 1). There arises the problem of the minimax testing of the hypothesis H₀: f() = p().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 115–125, 1990.