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Information in a scheme with additive noise

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Abstract

A formula is proved expressing the information contained in a stationary, linearly regular, Gaussian process with an independent additive increment relative to the original unperturbed process.

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Literature cited

  1. I. M. Gel'fand and A. M. Yaglom, “On the computation of the amount of information of a random function contained in another such function,” Usp. Mat. Nauk,12, No.l (1957).

  2. V. N. Solev, “On the average amount of information per unit time contained in a Gaussian stationary process relative to another process,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst.,29, (1972).

  3. K. Hofman, Banach Spaces of Analytic Functions [Russian translation], IL, Moscow (1963).

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  4. Yu. A. Rozanov, Stationary Stochastic Processes, Moscow (1964).

  5. V. N. Solev, “On a continual analogue of a theorem of G. Szegö,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst.,39 (1974).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 55, pp. 117–127, 1976.

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Solev, V.N. Information in a scheme with additive noise. J Math Sci 16, 996–1004 (1981). https://doi.org/10.1007/BF01676143

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  • DOI: https://doi.org/10.1007/BF01676143

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