"Rough path theory, differential equations and stochastic analysis"


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 Nazionalità Coordinatore Germany [DE]
 Totale costo 850˙820 €
 EC contributo 850˙820 €
 Programma 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)
 Code Call ERC-2010-StG_20091028
 Funding Scheme ERC-SG
 Anno di inizio 2010
 Periodo (anno-mese-giorno) 2010-09-01   -   2016-08-31


# participant  country  role  EC contrib. [€] 

 Organization address address: Rudower Chaussee 17
city: BERLIN
postcode: 12489

contact info
Titolo: Dr.
Nome: Friederike
Cognome: Schmidt-Tremmel
Email: send email
Telefono: +49 30 63923481
Fax: +49 30 63923333

DE (BERLIN) beneficiary 172˙943.70

 Organization address address: STRASSE DES 17 JUNI 135
city: BERLIN
postcode: 10623

contact info
Titolo: Ms.
Nome: Silke
Cognome: Hönert
Email: send email
Telefono: +49 30 31479973
Fax: +49 30 31421689

DE (BERLIN) hostInstitution 677˙876.30

 Organization address address: STRASSE DES 17 JUNI 135
city: BERLIN
postcode: 10623

contact info
Titolo: Prof.
Nome: Peter Karl
Cognome: Friz
Email: send email
Telefono: 493031000000

DE (BERLIN) hostInstitution 677˙876.30


 Word cloud

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related    lyons    equations    partial       theory    stochastic    viscosity    rough       path    wise    differential    smoothness    continuous   

 Obiettivo del progetto (Objective)

'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).'

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