Opendata, web and dolomites


Geometric aspects in pathwise stochastic analysis and related topics

Total Cost €


EC-Contrib. €






Project "GPSART" data sheet

The following table provides information about the project.


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

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Project website
 Total cost 1˙465˙000 €
 EC max contribution 1˙465˙000 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-CoG
 Funding Scheme ERC-COG
 Starting year 2016
 Duration (year-month-day) from 2016-09-01   to  2021-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    TECHNISCHE UNIVERSITAT BERLIN DE (BERLIN) coordinator 1˙180˙000.00
2    FORSCHUNGSVERBUND BERLIN EV DE (BERLIN) participant 285˙000.00


 Project objective

'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 writer of these lines (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 of important 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 rough 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.'


year authors and title journal last update
List of publications.
2019 Ilya Chevyrev, Peter K. Friz, Alexey Korepanov, Ian Melbourne
Superdiffusive limits for deterministic fast-slow dynamical systems
published pages: , ISSN: , DOI:
2018 C. Bayer, P. K. Friz, A. Gulisashvili, B. Horvath, B. Stemper
Short-time near-the-money skew in rough fractional volatility models
published pages: 779-798, ISSN: 1469-7688, DOI: 10.1080/14697688.2018.1529420
Quantitative Finance 19/5 2019-09-09
2017 Christian Bayer, Peter K. Friz, Paul Gassiat, Joerg Martin, Benjamin Stemper
A regularity structure for rough volatility
published pages: , ISSN: , DOI:
2018 Friz, Peter K.; Gassiat, Paul; Pigato, Paolo
Precise asymptotics: robust stochastic volatility models
published pages: , ISSN: , DOI:
1 2019-09-09
2018 Tran, Huy; Yuan, Yizheng
A support theorem for SLE curves
published pages: , ISSN: , DOI:
1 2019-09-09
2019 Coghi, Michele; Deuschel, Jean-Dominique; Friz, Peter; Maurelli, Mario
Pathwise McKean-Vlasov Theory
published pages: , ISSN: , DOI:
1 2019-09-09
2019 Khalil Chouk, Willem van Zuijlen
Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions
published pages: , ISSN: , DOI:
2018 Peter K. Friz, David J. Prömel
Rough path metrics on a Besov–Nikolskii-type scale
published pages: 8521-8550, ISSN: 0002-9947, DOI: 10.1090/tran/7264
Transactions of the American Mathematical Society 370/12 2019-09-09
2019 Chevyrev, Ilya; Friz, Peter K.; Korepanov, Alexey; Melbourne, Ian; Zhang, Huilin
Deterministic homogenization for discrete-time fast-slow systems under optimal moment assumptions
published pages: , ISSN: , DOI:
1 2019-09-09
2019 Peter K. Friz, Huy Tran, Yizheng Yuan
Regularity of the Schramm-Loewner field and refined Garsia-Rodemich-Rumsey estimates
published pages: , ISSN: , DOI:
published pages: , ISSN: 2050-5094, DOI: 10.1017/fms.2019.3
Forum of Mathematics, Sigma 7 2019-09-05
published pages: , ISSN: 2050-5094, DOI: 10.1017/fms.2017.18
Forum of Mathematics, Sigma 5 2019-06-18
2018 Jean-Dominique Deuschel, Peter K. Friz, Mario Maurelli, Martin Slowik
The enhanced Sanov theorem and propagation of chaos
published pages: 2228-2269, ISSN: 0304-4149, DOI: 10.1016/
Stochastic Processes and their Applications 128/7 2019-06-18
2017 Peter K. Friz, Paul Gassiat, Pierre-Louis Lions, Panagiotis E. Souganidis
Eikonal equations and pathwise solutions to fully non-linear SPDEs
published pages: 256-277, ISSN: 2194-0401, DOI: 10.1007/s40072-016-0087-9
Stochastics and Partial Differential Equations: Analysis and Computations 5/2 2019-06-18
2019 Y. Bruned, I. Chevyrev, P.K. Friz, R. Preiß
A rough path perspective on renormalization
published pages: 108283, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2019.108283
Journal of Functional Analysis 60 2019-09-05

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