Mathematisches Kolloquium

Zusammenfassung: In 1961, Ciesielski established a remarkable isomorphism of spaces of Hölder continuous functions and Banach spaces of real valued se- quences. The isomorphism can be established along Fourier type ex- pansions of (rough) Holder 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. In a more general and analytical setting, this pathwise approach of rough path analysis can be understood in terms of Paley-Littlewood de- compositions of distributions, and Bony paraproducts in Besov spaces. It allows a smooth approach of formal products of singular distributions, and consequently of SPDE with rough and multiplicative noise. Also, pathwise solutions of BSDE are in reach. This talk is based on work with M. Gubinelli (U Bonn) and N. Perkowski (HU Berlin).

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