On the Continuity of the Cramer TransformReportar como inadecuado




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Abstract : The Cramer transform introduced in large deviations theory sends classical probabilities resp. finite positive measures into min,+ probabilities resp. finite measures also called cost measures. We study its continuity when the two spaces of measures are endowed with the weak convergence topology. We prove that the Cramer transform is continuous in the subspace of logconcave measures and show counter examples in the opposite case. Moreover, in finite dimension, the Cramer transform is bicontinuous. Then, logconcave measures may be identified with lower semicontinuous convex functions.

Keywords : FENCHEL TRANSFORM WEAK CONVERGENCE LARGE DEVIATIONS IDEMPOTENT MEASURE LOGCONCAVE MEASURE CRAMER TRANSFORM LOGCONCAVE FUNCTION MAX-PLUS ALGEBRA





Autor: Marianne Akian -

Fuente: https://hal.archives-ouvertes.fr/



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