Objetivo We propose to study stochastic (classical and partial) differential equations and various topics of stochastic analysis, with particular focus on the interplay with T. Lyons' rough path theory:1) There is deep link, due to P. Malliavin, between the theory of hypoelliptic second order partial differential operators and certain smoothness properties of diffusion processes, constructed via stochastic differential equations. There is increasing evidence (F. Baudoin, M. Hairer &) that a Markovian (=PDE) structure is dispensable and that Hoermander type results are a robust feature of stochastic differential equations driven by non-degenerate Gaussian processes; many pressing questions have thus appeared.2) We return to the works of P.L. Lions and P. Souganidis (1998-2003) on a path-wise theory of fully non-linear stochastic partial differential equations in viscosity sense. More specifically, we propose a rough path-wise theory for such equations. This would in fact combine the best of two worlds (the stability properties of viscosity solutions vs. the smoothness of the Ito-map in rough path metrics) to the common goal of the analysis of stochastic partial differential equations. On a related topic, we have well-founded hope that rough paths are the key to make the duality formulation for control problems a la L.C.G. Rogers (2008) work in a continuous setting.3) Rough path methods should be studied in the context of (not necessarily continuous) semi-martingales, bridging the current gap between classical stochastic integration and its rough path counterpart. Related applications are far-reaching, and include, as conjectured by J. Teichmann, Donsker type results for the cubature tree (Lyons-Victoir s powerful alternative to Monte Carlo). Ámbito científico natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Convocatoria de propuestas ERC-2010-StG_20091028 Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida TECHNISCHE UNIVERSITAT BERLIN Aportación de la UE € 677 876,29 Dirección STRASSE DES 17 JUNI 135 10623 Berlin Alemania Ver en el mapa Región Berlin Berlin Berlin Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Silke Hönert (Ms.) Investigador principal Peter Karl Friz (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (2) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo TECHNISCHE UNIVERSITAT BERLIN Alemania Aportación de la UE € 677 876,29 Dirección STRASSE DES 17 JUNI 135 10623 Berlin Ver en el mapa Región Berlin Berlin Berlin Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Silke Hönert (Ms.) Investigador principal Peter Karl Friz (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos FORSCHUNGSVERBUND BERLIN EV Alemania Aportación de la UE € 172 943,71 Dirección RUDOWER CHAUSSEE 17 12489 Berlin Ver en el mapa Región Berlin Berlin Berlin Tipo de actividad Research Organisations Contacto administrativo Friederike Schmidt-Tremmel (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
