On Riemann-Liouville type operators, bmo, and gradient estimates on the Wiener space
Abstract: We discuss in a stochastic framework the interplay between
Riemann-Liouville type operators applied to stochastic processes,
bounded mean oscillation, real interpolation, and approximation.
In particular, we investigate the singularity of gradient processes on the Wiener space arising from parabolic PDEs via the Feynman-Kac theory.
The singularity is measured in terms of bmo-conditions on the fractional integrated gradient. As an application we provide a discrete time hedging strategy for the binary option with a uniform local control of the hedging error under a shortfall constraint.
[1] Stefan Geiss and Nguyen Tran Thuan: On Riemann-Liouville type
operators, bmo, gradient estimates on the Wiener space, and
approximation. In revision, 2024.
