Maximum Entropy in the Finite Stielties and Hamburger Moment Problem
نویسنده
چکیده
A necessary and suucient condition for the existence of the maximum entropy (ME) function deened in an innnite or semiinnnite interval, is provided. The conclusions reached show that, except in a few particular cases, the necessary and suucient conditions for the existence of maximum entropy function are identical to the conditions for the solution of the moment problem when the rst M+1 moments are assigned. Even if the conclusions reached are very similar to the Hausdorr case, the speciicity of the Hamburger and Stieltjes cases demands a diierent handling. A suucient condition for the entropy convergence of the resulting sequence of maximum entropy estimators to the entropy of the recovering function is also provided.
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