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Geometric aspects in pathwise stochastic analysis and related topics

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Publications

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
DOI: 10.1007/s00440-020-00988-5

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
DOI: 10.1214/20-ejp425

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
DOI: 10.1007/s00440-021-01058-0

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
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
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
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
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
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
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
DOI: 10.1214/20-aap1560

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
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
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
DOI: 10.1111/mafi.12233

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

Author(s): Friz, Peter K.; Klose, Tom
Published in: Issue 4, 2021

A support theorem for SLE curves

Author(s): Tran, Huy; Yuan, Yizheng
Published in: Issue 1, 2018

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: Issue 1, 2019

Regularity of the Schramm-Loewner field and refined Garsia-Rodemich-Rumsey estimates

Author(s): Peter K. Friz, Huy Tran, Yizheng Yuan
Published in: 2019

Superdiffusive limits for deterministic fast-slow dynamical systems

Author(s): Ilya Chevyrev, Peter K. Friz, Alexey Korepanov, Ian Melbourne
Published in: 2019

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
DOI: 10.1007/978-3-030-41556-3

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
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
DOI: 10.1214/20-aop1497

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
DOI: 10.1007/978-3-030-15338-0_2