The wavelet transform for Wiener functionals and some applications

Abstract

The wavelet transform is defined for Wiener functionals. We characterize global and local regularities of Wiener functionals and we give a criterion for the existence and regularity of densities. Such a criterion is applied to diffusion processes and to the solutions to backward stochastic differential equations.

Keywords::

• wavelet transform
• Wiener analysis
• Malliavin calculus
• diffusion processes
• backward stochastic differential equations

MSC (2010) Classification::

• 60H