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

ENTROPIE DES PROCESSUS LIN…AIRES

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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