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Contents of PMS, Vol. 11, Fasc. 1,
pages 79 - 95
 

ENTROPIE DES PROCESSUS LINÉAIRES

Abdelkader Mokkadem

Abstract: Let Y = (Yn)n (- Z be a real stationary process with the spectral representation

integral p inc Yn = -pe dZY
and X = (Xn)n( - Z be a process defined by

integral p inc Xn = e f(c)dZY . -p

We prove that the entropy of X satisfies the relation

integral -1- p H(X) > 2p -p Log| f(c)|dc+ H(Y ).

Some cases where equality holds are obtained. We also give some applications.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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