Geometric aspects in pathwise stochastic analysis and related topics

Project Information

GPSART

Grant agreement ID: 683164

DOI

10.3030/683164

Project closed

EC signature date 10 May 2016

Start date 1 September 2016

End date 31 August 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 465 000,00

EU contribution

€ 1 465 000,00

Coordinated by

TECHNISCHE UNIVERSITAT BERLIN
Germany

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (29)

Short dated smile under Rough Volatility: asymptotics and numerics

Author(s): Friz, Peter K.; Gassiat, Paul; Pigato, Paolo
Published in: Quantitative Finance, Issue 22:3, 463-480, 2022, 2022, ISSN 1469-7688
Publisher: Institute of Physics Publishing
DOI: 10.1080/14697688.2021.1999486

Superdiffusive limits for deterministic fast–slow dynamical systems

Author(s): Ilya Chevyrev, Peter K. Friz, Alexey Korepanov, Ian Melbourne
Published in: Probability Theory and Related Fields, Issue 178/3-4, 2020, Page(s) 735-770, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-020-00988-5

Forests, Cumulants, Martingales

Author(s): Peter K. Friz; Jim Gatheral; Radoš Radoičić
Published in: Ann. Probab., Issue 50(4): 1418-1445 (July 2022), 2022, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/21-aop1560

Couplings via Comparison Principle and Exponential Ergodicity of SPDEs in the Hypoelliptic Setting

Author(s): Oleg Butkovsky, Michael Scheutzow
Published in: Commun. Math. Phys., Issue 379, 1001–1034 (2020)., 2020, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-020-03834-w

The moving frame method for iterated-integrals: orthogonal invariants

Author(s): Diehl, Joscha; Preiß, Rosa; Ruddy, Michael; Tapia, Nikolas
Published in: Foundations of Computational Mathematics, Issue 2022, 2022, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-022-09569-5

A support theorem for SLE curves

Author(s): Huy Tran, Yizheng Yuan
Published in: Electronic Journal of Probability, Issue 25/none, 2020, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-ejp425

Approximation of SDEs: a stochastic sewing approach

Author(s): Oleg Butkovsky, K. Dareiotis, K., M. Gerencsér,
Published in: Probab. Theory Relat. Fields, Issue 181, 975–1034 (2021), 2021, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-021-01080-2

Differential equations driven by rough paths with jumps

Author(s): Peter K. Friz; Huilin Zhang; Huilin Zhang
Published in: Journal of Differential Equations, Issue Volume 264, 2018, 2018, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2018.01.031

Precise Laplace asymptotics for singular stochastic PDEs: The case of 2D gPAM

Author(s): Friz, Peter K.; Klose, Tom
Published in: J. Funct. Anal., Issue 109446, 2022, 2021, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2022.109446

Regularity of SLE in $$(t,\kappa )$$ and refined GRR estimates

Author(s): Peter K. Friz, Huy Tran, Yizheng Yuan
Published in: Probability Theory and Related Fields, Issue 180/1-2, 2021, Page(s) 71-112, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-021-01058-0

Smooth Rough Paths, Their Geometry and Algebraic Renormalization

Author(s): Carlo Bellingeri; Peter K. Friz; Sylvie Paycha; Rosa Preiß
Published in: Vietnam J. Math., Issue 50, 719–761 (2022), 2022, ISSN 2305-221X
Publisher: Springer Science + Business Media
DOI: 10.1007/s10013-022-00570-7

Support theorem for a singular SPDE: The case of gPAM

Author(s): Khalil Chouk, Peter Friz
Published in: Ann. Inst. H. Poincaré Probab. Statist., 2018, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/16-aihp800

Besov rough path analysis

Author(s): Peter K. Friz; Benjamin Seeger; Pavel Zorin-Kranich
Published in: Journal of Differential Equations, Issue Volume 339, 2022,, 2022, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2022.08.008

Malliavin calculus for regularity structures: The case of gPAM

Author(s): Giuseppe Cannizzaro; Peter K. Friz; Paul Gassiat
Published in: Journal of Functional Analysis, Issue 2017, 272, pp.363 - 419, 2017, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2016.09.024

Eikonal equations and pathwise solutions to fully non-linear SPDEs

Author(s): Peter K. Friz, Paul Gassiat, Pierre-Louis Lions, Panagiotis E. Souganidis
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, Issue 5/2, 2017, Page(s) 256-277, ISSN 2194-0401
Publisher: Springer
DOI: 10.1007/s40072-016-0087-9

The enhanced Sanov theorem and propagation of chaos

Author(s): Jean-Dominique Deuschel, Peter K. Friz, Mario Maurelli, Martin Slowik
Published in: Stochastic Processes and their Applications, Issue 128/7, 2018, Page(s) 2228-2269, ISSN 0304-4149
Publisher: Elsevier BV
DOI: 10.1016/j.spa.2017.09.010

ON THE REGULARITY OF SLE TRACE

Author(s): PETER K. FRIZ, HUY TRAN
Published in: Forum of Mathematics, Sigma, Issue 5, 2017, ISSN 2050-5094
Publisher: CUP
DOI: 10.1017/fms.2017.18

VARIETIES OF SIGNATURE TENSORS

Author(s): CARLOS AMÉNDOLA, PETER FRIZ, BERND STURMFELS
Published in: Forum of Mathematics, Sigma, Issue 7, 2019, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2019.3

A rough path perspective on renormalization

Author(s): Y. Bruned, I. Chevyrev, P.K. Friz, R. Preiß
Published in: Journal of Functional Analysis, Issue 60, 2019, Page(s) 108283, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2019.108283

Rough path metrics on a Besov–Nikolskii-type scale

Author(s): Peter K. Friz, David J. Prömel
Published in: Transactions of the American Mathematical Society, Issue 370/12, 2018, Page(s) 8521-8550, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7264

Pathwise McKean–Vlasov theory with additive noise

Author(s): Michele Coghi, Jean-Dominique Deuschel, Peter K. Friz, Mario Maurelli
Published in: The Annals of Applied Probability, Issue 30/5, 2020, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-aap1560

Deterministic homogenization for discrete-time fast-slow systems under optimal moment assumptions

Author(s): Chevyrev, Ilya; Friz, Peter K.; Korepanov, Alexey; Melbourne, Ian; Zhang, Huilin
Published in: Ann. Inst. H. Poincaré Probab. Statist., Issue 58(3): 1328-1350, 2022, 2022, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/21-aihp1203

Short-time near-the-money skew in rough fractional volatility models

Author(s): C. Bayer, P. K. Friz, A. Gulisashvili, B. Horvath, B. Stemper
Published in: Quantitative Finance, Issue 19/5, 2018, Page(s) 779-798, ISSN 1469-7688
Publisher: Institute of Physics Publishing
DOI: 10.1080/14697688.2018.1529420

Canonical RDEs and general semimartingales as rough paths

Author(s): Ilya Chevyrev, Peter K. Friz
Published in: The Annals of Probability, Issue 47/1, 2019, Page(s) 420-463, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/18-aop1264

A regularity structure for rough volatility

Author(s): Christian Bayer, Peter K. Friz, Paul Gassiat, Jorg Martin, Benjamin Stemper
Published in: Mathematical Finance, Issue 30/3, 2020, Page(s) 782-832, ISSN 0960-1627
Publisher: Blackwell Publishing Inc.
DOI: 10.1111/mafi.12233

Unified signature cumulants and generalized Magnus expansions

Author(s): Peter K. Friz; Paul P. Hager; Nikolas Tapia
Published in: Forum of Mathematics, Sigma,, Issue 10, E42., 2022, ISSN 2050-5094
Publisher: Cambridge
DOI: 10.1017/fms.2022.20

A McKean-Vlasov SDE and particle system with interaction from reflecting boundaries

Author(s): Michele Coghi; Wolfgang Dreyer; Peter K. Friz; Paul Gajewski; Clemens Guhlke; Mario Maurelli
Published in: SIAM Journal on Mathematical Analysis, Issue Vol. 54, Iss. 2 (2022), 2022, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1409421

Singular paths spaces and applications

Author(s): Carlo Bellingeri; Peter K. Friz; Máté Gerencsér
Published in: Stochastic Analysis and Applications,, Issue 40:6, 1126-1149, 2022., 2022, ISSN 0736-2994
Publisher: Marcel Dekker Inc.
DOI: 10.1080/07362994.2021.1988641

Transport and continuity equations with (very) rough noise

Author(s): Carlo Bellingeri; Ana Djurdjevac; Peter K. Friz; Nikolas Tapia
Published in: SN Partial Differential Equations and Applications Partial Differ. Equ. Appl., Issue 2, 49 (2021), 2021, ISSN 2662-2963
Publisher: Springer
DOI: 10.1007/s42985-021-00101-y

Other (5)

Rough semimartingales and $p$-variation estimates for martingale transforms

Author(s): Friz, Peter and Zorin-Kranich, Pavel
Published in: to appear Annals of Probability, Issue arXiv, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2008.08897

Rough stochastic differential equations

Author(s): Peter K. Friz, Antoine Hocquet, Khoa Lê
Published in: arXiv, Issue 2022, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2106.10340

ALMOST SURE DIFFUSION APPROXIMATION IN AVERAGINGVIA ROUGH PATHS THEORY

Author(s): Peter Friz, Yuri Kifer
Published in: arXiv, Issue 2022, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2111.05390

Law of the SLE tip

Author(s): Oleg Butkovsky, Vlad Margarint, Yizheng Yuan
Published in: to appear EJP, Issue 2021, 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2110.11247

Well-posedness of stochastic heat equation with distributional drift and skew stochastic heat equation

Author(s): Athreya, Siva; Butkovsky, Oleg; L��, Khoa; Mytnik, Leonid
Published in: to appear in CPAM, Issue 2023 (tbc), 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2011.13498

Monographic books (1)

A Course on Rough Paths - With an Introduction to Regularity Structures

Author(s): P. Friz and M. Hairer
Published in: Issue Second edition of [Friz-Hairer; Universitext. Springer, Cham; 2014],, 2020, Page(s) 1-346, ISBN 978-3-030-41556-3
Publisher: Springer
DOI: 10.1007/978-3-030-41556-3

Non-peer reviewed articles (2)

Precise asymptotics: Robust stochastic volatility models

Author(s): P. K. Friz, P. Gassiat, P. Pigato
Published in: The Annals of Applied Probability, Issue 31/2, 2021, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-aap1608

Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions

Author(s): Khalil Chouk, Willem van Zuijlen
Published in: The Annals of Probability, Issue 49/4, 2021, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-aop1497

Book chapters (1)

Multiscale Systems, Homogenization, and Rough Paths

Author(s): Ilya Chevyrev, Peter K. Friz, Alexey Korepanov, Ian Melbourne, Huilin Zhang
Published in: Probability and Analysis in Interacting Physical Systems - In Honor of S.R.S. Varadhan, Berlin, August, 2016, Issue 283, 2019, Page(s) 17-48, ISBN 978-3-030-15337-3
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-15338-0_2