This is the web portal of the ERC project Geometric aspects in pathwise stochastic analysis and related topics (GPSART, Sep 2016 - Aug 2022)
For some soft information about the project (in German) click here, or click here for some official ERC infos.
Summary and overall objectives of the project (For the final period, include the conclusions of the action)
Recent years have seen an explosion of applications of geometric and pathwise ideas in probability theory, with motivations from fields as diverse as quantitative finance, statistics, filtering, control theory and statistical physics. Much can be traced back to Bismut, Malliavin (1970s) on the one-hand and then Doss, Sussman (1970s), Foellmer (1980s) on the other hand, with substantial new input from Lyons (from '94 on), followed by a number of workers, including Gubinelli (from '04 on) and the PI of this project (also from '04 on). Most recently, the theory of such ``rough paths" has been extended to ``rough fields", notably in the astounding works of M. Hairer (from '13 on). The purpose of this project is to study a number ofimportant problems in this field, going beyond the rough path setting, and with emphasis on geometric ideas.
(i) The transfer of concepts from rough path theory to the new world of Hairer's regularity structures.
(ii) Applications of geometric and pathwise ideas in quantitative finance.
(iii) Obtain a pathwise understanding of the geometry of Loewner evolution and more generally explore the use of rougg path-inspired ideas in the world of Schramm-Loewner evolution.
(iv) Investigate the role of geometry in the pathwise analysis of non-linear evolution equations.
Related key publication (selection, August 2021; present/previous ERC staff members in bold)
UPDATE 30-Nov-2022: COMPLETE PUBLICATION LIST
A Course on Rough Paths - With an Introduction to Regularity Structures, 2nd edition; P. Friz and M. Hairer; Springer (2020)
A rough path perspective on renormalization; Y. Bruned, I. Chevyrev, P.K. Friz, R. Preiß; Journal of Functional Analysis (2019)
VARIETIES OF SIGNATURE TENSORS; AMÉNDOLA, C., FRIZ, P., STURMFELS, B. (2019); Forum of Mathematics, Sigma (2019)
A regularity structure for rough volatility; Christian Bayer, Peter K. Friz, Paul Gassiat, Jorg Martin, Benjamin Stemper; Mathematical Finance (2019)
Precise asymptotics: Robust stochastic volatility models; P. K. Friz, P. Gassiat, P. Pigato; The Annals of Applied Probability (2020)
On the regularity of SLE trace, P. Friz, H. Tran, Forum of Mathematics, Sigma (2017)
Regularity of SLE and refined GRR estimates. Friz, P.K., Tran, H., Yuan, Y.; Probab. Theory Relat. Fields (2021)
Eikonal equations and pathwise solutions to fully non-linear SPDEs. Friz, Peter K., Gassiat, Paul, Lions, Pierre-Louis, Souganidis, Panagiotis E.; Stochastics and Partial Differential Equations: Analysis and Computations (2017)
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OPEN ACCESS! All papers funded by this project are available (in final form) on the arXiv,
In many cases also by publisher open access, e.g. in the context of project DEAL.
Links: arXiv repository, MathScinet (subscribers only ...) and Google Scholar.
ERC Consolidator Grant 2015
Action Acronym: GPSART
Action Number: 683164
Action Title: Geometric aspects in pathwise stochastic analysis and related topics
Principal Investigator: Peter K. Friz
Host Institution: TU Berlin
Additional beneficiaries: Forschungsverbund Berlin e.V. (WIAS)
Starting date: Sep 2016
Project Duration: 6 years
Potential postdocs:
Expressions of interests always welcome, please email friz[you know what]math.tu-berlin.de
Other links of interest:
DFG research unit (2016-2019) Rough paths, stochastic partial differential equations and related topics
ERC Starting Grant (2010-2016) Rough path theory, differential equations and stochastic analysis
P. K. Friz - TU Berlin homepage