The minimizer P* of the I-divergence I(P∥Q) for P in a set Π defined by linear constraints is known to he mutually absolutely continuous with Q (P* ≡ Q) providing a P̃ in Π exists with P̃ ≡ Q and I(P̃∥Q) < ∞. We ask when the existence of P̄ and P, both in Π, with P̄ Q and I(P∥Q) < ∞ is already sufficient for P* ≡ Q. We give a positive answer for measures on a product space when Π is determined by prescribing the two marginals.
|Number of pages||10|
|Journal||Studia Scientiarum Mathematicarum Hungarica|
|Publication status||Published - Dec 1 1998|
- Iterative scaling
- Schrödinger's problem
- Specified marginals
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