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...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2013
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| Sorozat: | Acta scientiarum mathematicarum
79 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/32912 |
| 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. |
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| Terjedelem/Fizikai jellemzők: | 687-714 |
| ISSN: | 0001-6969 |