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Entropy of stochastic processes homogeneous with respect to a commutative group of transformations

✍ Scribed by B. S. Pitskel


Publisher
SP MAIK Nauka/Interperiodica
Year
1978
Tongue
English
Weight
547 KB
Volume
23
Category
Article
ISSN
0001-4346

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It is shown that for a real orthogonal matrix A, a real number r ∈ (0; 2), and two i.i.d. random vectors X and Y , the inequality E X -AY r ¿ E X -Y r is valid, with equality if and only if the distribution of X is invariant with respect to the group generated by the matrix A. Some generalizations o