(Last update: 11/2018)
Publications
C. Bayer, P. K. Friz, S. Riedel, J. Schoenmakers: From rough path estimates to multilevel Monte Carlo (SIAM Journal on Numerical Analysis, Volume 54, Number 3 (2016), Pages 1449-1483)
G. Cannizzaro, P. K. Friz, P. Gassiat: Malliavin calculus for regularity structures: the case of gPAM (J. Func. Ana.Vol 272, Issue 1, 2017, 363–419)
K. Chouk, P. K. Friz: Support theorem for a singular SPDE: the case of gPAM (to appear: Annals IHP)
P. K. Friz, P. Gassiat, P.-L. Lions, P. E. Souganidis: Eikonal equations and pathwise solutions to fully non-linear SPDEs (to appear Stoch PDE: Anal Comp)
S. Riedel, M. Scheutzow: Rough differential equations with unbounded drift term (Journal of Differential Equations, Volume 262, Issue 1 (2017), Pages 283-312.)
P. K. Friz, A. Shekhar: General rough integration, Lévy rough paths and a Lévy-Kintchine type formula (to appear: Ann. Proba.)
M. Gubinelli, N. Perkowski: KPZ Reloaded (Communications in Mathematical Physics, 2017, Vol. 349, no.1, 165-269)
M. Gubinelli, N. Perkowski: The Hairer-Quastel invariance principle at stationarity (RIMS Kôkyûroku Bessatsu B59, 2016)
I. Bailleul, S. Riedel, M. Scheutzow: Random dynamical systems, rough paths and rough flows (Journal of Differential Equations, Volume 262, Issue 12 (2017), Pages 5792-5823.)
S. Riedel: Transportation-cost inequalities for diffusions driven by Gaussian processes (Electronic Journal of Probability, Volume 22 (2017), Article 24, Pages 1-26.)
J. Diehl, M. Gubinelli, N. Perkowski (2017): The Kardar-Parisi-Zhang equation as scaling limit of weakly asymmetric interacting Brownian motions, Comm. Math. Phys., 354(2):549-589
K. Chouk, J. Gairing, N. Perkowski (2017): An invariance principle for the two-dimensional parabolic Anderson model with small potential, Stoch PDE: Anal Comp, 5(4), 520–558
R. Kruse, Y. Wu: Error analysis of randomized Runge-Kutta methods for differential equations with time-irregular coefficients (Comput. Meth. Appl. Math., Volume 17, Issue 3 (2017), Pages 479-498.)
Flandoli, F., Gess, B., and Scheutzow, M. (2017):
Synchronization by noise, Probab. Theory Related Fields, 168(3-4), 511-556, DOI: 10.1007/s00440-016-0716-2.
Flandoli, F., Gess, B., and Scheutzow, M. (2017):
Synchronization by noise for order-preserving random dynamical systems, Ann. Probab., 45(2), 1325-1350, DOI: 10.1214/16-AOP1088.
Scheutzow, M., Schulze, S. (2017):
Strong completeness and stochastic semi-flows for stochastic differential equations with monotone drift. J. Math. Anal. Appl., 446(2), 1555-1570, DOI: 10.1016/j.jmaa.2016.09.049.
Butkovsky, O., Scheutzow, M. (2017):
Invariant measures for stochastic functional differential equations, Electronic J. Probab., 22(98), 1-23, DOI: 10.1214/17-EJP122.
M. Biskup, W. Konig and R.S. dos Santos, Mass concentration and aging in thep arabolic Anderson model with doubly-exponential tails, Probab. Theory Relat. Fields 171:251-331, 2018.
Kruse, R., Scheutzow, M. (2018):
A discrete stochastic Gronwall lemma, Math. Comput. Simulation, 143, 149-157, DOI: 10.1016/j.matcom.2016.07.002.
Kulik, A., Scheutzow, M. (2018):
Generalized couplings and convergence of transition probabilities, Probab. Theory Related Fields, 171(1-2), 333-376, DOI: 10.1007/s00440-017-0779-8.
J.-D. Deuschel, P. K. Friz, M. Maurelli, M. Slowik (2018): The enhanced Sanov theorem and robust propagation of chaos, Stochastic Processes and their Applications, Volume 128, Issue 7, Pages 2228-2269,
Crauel, H., Scheutzow, M. (2018):
Minimal random attractors, J. Differential Equations, 265(2), 702-718, DOI: 10.1016/j.jde.2018.03.011.
P. Clavier, L. Guo, S. Paycha, B. Zhang (2018+), An algebraic formulation of the locality principle , to appear in European Journal of Mathematics
M. Gubinelli, N. Perkowski (2018), Energy solutions of KPZ are unique, J. Amer. Math. Soc., 31(2):427-471
P. Friz, H. Zhang (2018), Differential equations driven by rough paths with jumps, Journal of Differential Equations, 264 (10): 6226-6301
A. Hocquet, M. Hofmanova (2018), An energy method for rough partial differential equations, Journal of Differential Equations, 265 (4):1407-1466
M. Gubinelli, N. Perkowski (2018): Probabilistic approach to the stochastic Burgers equation, Stochastic Partial Differential Equations and Related Fields. In Honor of Michael Röckner
M. Gubinelli, N. Perkowski (2018): An introduction to singular SPDEs, Stochastic Partial Differential Equations and Related Fields. In Honor of Michael Röckner
I. Chevyrev, P. Friz (2018+), Canonical RDEs and general semimartingales as rough paths, to appear in Annals of Probability
J. Martin, N. Perkowski (2018+): Paracontrolled distributions on Bravais lattices and weak universality of the 2d parabolic Anderson model, to appear in Annales de l’Institut Henri Poincaré - Probabilités et Statistiques
M. Hofmanová, J-M. Leahy, T. Nilssen: On the Navier-Stokes equation perturbed by rough transport noise Journal of Evolution Equations, (2018). https://doi.org/10.1007/s00028-018-0473-z
A. Hocquet, T. Nilssen, W. Stannat: Generalized Burgers equation with rough transport noise , to appear in Stochastic Processes and their Applications.
Preprints
A. Deya, M. Gubinelli, M. Hofmanova, S. Tindel: General a priori estimates for rough PDEs with application to rough conservation laws (arXiv Apr 2016; accepted subject to revision JFA)
A. Deya, M. Gubinelli, M. Hofmanova, S. Tindel: One-dimensional reflected rough differential equations (arXiv Nov 2016)
I. Bailleul, A. Debussche, M. Hofmanova: Quasilinear generalized parabolic Anderson model equation (arXiv Nov 2016)
Y. Bruned, I. Chevyrev, P. K. Friz, R. Preiss: A Rough Path Perspective on Renormalization (arXiv Jan 2017; accepted subject to revision JFA)
Y. Bruned, I. Chevyrev, P. K. Friz: Examples of renormalized SDEs (arXiv Jan 2017)
R. Kruse, Y. Wu: A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients (arXiv Jun 2017)
M. Eisenmann, M. Kovács, R. Kruse, S. Larsson: On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients (arXiv Sep 2017)
I. Chevyrev, P. Friz, A. Korepanov, I. Melbourne, H. Zhang: Multiscale systems, homogenization, and rough paths (arXiv Dec 2017)
P. Goncalves, N. Perkowski, M. Simon: Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEP. (arXiv Oct 2017)
M. Eisenmann, R. Kruse: Two quadrature rules for stochastic Itō-integrals with fractional Sobolev regularity (arXiv Dec 2017)
R. Kruse, Y. Wu: A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations (arXiv Jan 2018)
T. Nilssen: Weak solutions of rough path SDE's via Girsanov (arXiv May 2018).
A. Hocquet, T. Nilssen: An Itô Formula for rough partial differential equations. Application to the maximum principle. (June 2018)
Butkovsky, O., Kulik, A., Scheutzow, M.: Generalized couplings and ergodic rates for SPDEs and other Markov models (arXiv January 2018).
C. Bayer, D. Belomestny, M. Redmann, S. Riedel, J. Schoenmakers. Solving linear parabolic rough partial differential equations (arXiv March 2018).
Jean-Dominique Deuschel and Tal Orenshtein. Scaling limit of wetting models in1 + 1 dimensions pinned to a shrinking strip. (arXiv 2018)
P. Friz, T. Nilssen, W. Stannat: Existence, uniqueness and stability of semi-linear rough partial differential equations (arXiv September 2018)
M. Gubinelli, N. Perkowski: The infinitesimal generator of the stochastic Burgers equation. (arXiv Oct 2018)
M. Hofmanová, J-M. Leahy, T. Nilssen: On a rough perturbation of the Navier-Stokes system and its vorticity formulation. (arXiv February 2019)
M. Coghi, T. Nilssen: Rough nonlocal diffusions. (arXiv May 2019)