In 1961, Ciesielski established a remarkable isomorphism of spaces of H%C3%B6lder continuous functions and Banach spaces of real valued sequences. The isomorphism can be established along Fourier type expansions of (rough) H%C3%B6lder continuous functions by means of the Haar-Schauder wavelet. We will start with 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 SPDE with rough and multiplicative noise. This course is based on work with M. Gubinelli (U Paris-Dauphine) and N. Perkowski (HU Berlin).

Course leader
Lecturer: Prof. Peter Imkeller (Institut fr Mathematik - Humboldt-Universitt zu Berlin, Germany)Coordinator: Prof. Stefan Geiss (University of Jyvskyl, Finland)

Target group
Basics of probability theory, stochastic processes and the to integral. The Summer School annually offers courses for advanced master's students, graduate students, and post-docs in the various fields of science and information technology.

Course aim
The most important aims of the Summer School are to develop post-graduates scientific readiness and to offer students the possibility to study in a modern, scientific environment and to create connections to the international science community.

Credits info
2 ECTS Passing: Obligatory attendance at lectures and completing the exercises.Grading: Pass/fail

Fee info
EUR 0: Participating the Summer School is free of charge, but student have to cover the costs of own travel, accommodation and meals at Jyvskyl.

Scholarships
The 25th Jyvskyl Summer School is not able to grant any Summer School students financial support. In order to ensure your participation, we recommend that you take steps to secure your own funding, for example, by turning first to your home institution

University of Jyv%C3%A4skyl%C3%A4
Address: Faculty of Mathematics and Science and Faculty of Information Technology, Jyv%C3%A4skyl%C3%A4 Summer School, Faculty of Mathematics and Science P.O.Box 35 (YK312), FIN-40014 University of Jyv%C3%A4skyl%C3%A4, Finland
Postal code: FIN-40014
City: Jyv%C3%A4skyl%C3%A4
Country: Finland
Website: http://www.jyu.fi/summerschool
E-mail: jss@jyu.fi
Phone: +358505818351