Quantization of Gaussian measures with Rényi-α-entropy constraints

We consider the optimal quantization problem with Renyi-aentropy constraints for centered Gaussian measures on a separable Banach space. For a = oo we can compute the optimal quantization error by a moment on a ball. For a £ ]1, oo] and large entropy bound we derive sharp asymptotics for the optimal...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerző: Kreitmeier Wolfgang
Dokumentumtípus: Cikk
Megjelent: Bolyai Institute, University of Szeged Szeged 2013
Sorozat:Acta scientiarum mathematicarum 79 No. 3-4
Kulcsszavak:Matematika
Tárgyszavak:
Online Access:http://acta.bibl.u-szeged.hu/32912
Leíró adatok
Tartalmi kivonat:We consider the optimal quantization problem with Renyi-aentropy constraints for centered Gaussian measures on a separable Banach space. For a = oo we can compute the optimal quantization error by a moment on a ball. For a £ ]1, oo] and large entropy bound we derive sharp asymptotics for the optimal quantization error in terms of the small ball probability of the Gaussian measure. We apply our results to several classes of Gaussian measures. The asymptotical order of the optimal quantization error for a > 1 is different from the well-known cases a = 0 and a = 1.
Terjedelem/Fizikai jellemzők:687-714
ISSN:0001-6969