2015Journal of Statistical Research of IranOpen access

The Rate of Entropy for Gaussian Processes

Leila Golshani

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Abstract

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates.Using that we can obtain Tsallis entropy rate for stationary Gaussian processes.Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian processes.

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In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates.Using that we can obtain Tsallis entropy rate for stationary Gaussian processes.Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian processes.

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Available abstract

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates.Using that we can obtain Tsallis entropy rate for stationary Gaussian processes.Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian processes.

Key concepts: Rényi entropy, Tsallis entropy, Entropy rate, Statistical physics, Mathematics, Shannon's source coding theorem, Maximum entropy thermodynamics, Gaussian

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