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

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