- Selfsimilariry, trees, branching and fragmentation
- Fractal objects fractional and multifractional processes
- Matrix valued selfsimilar processes
- Stochastic Löwner evolution
- Selfsimilar Markov processes
- Selfsimilarity in finance
Self-similarity is the property which certain stochastic processes have of preserving their distribution under a time-scale change. This property appears in all areas of probability theory and offers a number of fields of application. The aim of this conference is to bring together the main representatives of different aspects of self-similarity currently being studied in order to promote exchanges on their recent research and enable them to share their knowledge with young researchers. The conference may be considered as a sequel to those organized in Clermont-Ferrand (2002) and Toulouse (2005).
Some classes of self-similar processes for which Brownian motion is a representative satisfy fractional and multifractional properties which may be applied to modeling of fractal physical phenomena. Other classes are composed of homogeneous or inhomogeneous Markov processes and are of particular interest both from a theoretical and an applied point of view because of their relation with Levy processes characterised by some pathway transformations. Objects such as random trees and fragmentation processes are usually represented in the self-similar case using self-similar Markov processes. Stochastic Löwner evolution and its applications to percolation constitutes a fundamental example in which the self-similarity property plays a predominant part. A series of lectures given every morning will enable each of these topics to be presented concisely to all the participants. Equal importance will be given to presentations centered on fundamental theoretical aspects and to talks which focus on applications.