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| In 1961, Ciesielski established a remarkable isomorphism of spaces of
H\"older continuous functions and Banach spaces of real valued sequences.
The isomorphism can be established along Fourier type expansions of (rough) H\"older continuous functions
by means of the Haar-Schauder wavelet. We will use Schauder representations for a
pathwise approach of the integral of one rough function with respect to another one, using Ciesielski's isomorphism. In a
more general and analytical setting, this pathwise approach of rough path
analysis can be understood in terms of Paley-Littlewood decompositions of
distributions, and Bony paraproducts in Besov spaces. It allows a smooth approach of formal products of singular distributions,
and consequently of BSDE with rough and multiplicative noise. This talk is based on
work in progress with M. Gubinelli (U Paris-Dauphine) and N. Perkowski (HU
Berlin). |
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