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A condition for the mutual absolute continuity of Gaussian measures, generated by a stationary process

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Abstract

One obtains an analytic condition for the absolute continuity of the Gaussian measures P t f , P t f* , corresponding to stationary processes on the interval [o,t] with spectral densities f and f*.

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Literature cited

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    M. G. Krein, “On the fundamental approximation problem in the theory of extrapolation and filtration of stationary random processes,” Dokl. Akad. Nauk SSSR,94 No. 1, 13–16 (1954).

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    L. de Branges, Hilbert Spaces of Entire Functions, Prentice-Hall, Englewood Cliffs (1968).

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    I. A. Ibragimov and Yu. A. Rozanov (Y. A. Rozanov), Gaussian Random Processes, Springer, New York (1978).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 160–163, 1985.

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Solev, V.N. A condition for the mutual absolute continuity of Gaussian measures, generated by a stationary process. J Math Sci 36, 546–548 (1987). https://doi.org/10.1007/BF01663469

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Keywords

  • Stationary Process
  • Spectral Density
  • Gaussian Measure
  • Absolute Continuity
  • Mutual Absolute Continuity