On fractional smoothness and Lp-approximation on the Gaussian space

• Geiss, Stefan ^[1] ; Toivola, Anni. ^[1]
  1. [1] University of Jyväskylä

     University of Jyväskylä

     Jyväskylä, Finlandia

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 2, 2015, págs. 605-638
• Idioma: inglés
• DOI: 10.1214/13-AOP884
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• Resumen

  • We consider Gaussian Besov spaces obtained by real interpolation and Riemann–Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in Lp for 2≤p<∞ for stochastic integrals with respect to the d-dimensional (geometric) Brownian motion.