Publications and Preprints

of Prof. Dr. Nicolas Perkowski

Publications

For the final versions please consult the journals.

2025
Fractional Kolmogorov equations with singular paracontrolled terminal conditions (with H. Kremp), accepted at Journal of Theoretical Probability (2025+)
Periodic homogenization for singular Lévy SDEs (with H. Kremp), accepted at Annales de l’Institut Henri Poincaré - Probabilités et Statistiques (2025+)
Level crossings of fractional Brownian motion (with P. Das, R. Lochowski, T. Matsuda), accepted at Annals of Probability (2025+)
The Compact Support Property of Rough Super Brownian Motion on IR^2 (with R. Jin), Stochastic Process and their Applications, 2025, Vol. 182. Published version.
2024
Almost Sure Asymptotic Stability of Parabolic SPDEs with Small Multiplicative Noise (with Y. Meng, N.Sri. Namachchivaya), Dynamical Systems, 2024. Published version.
Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation (with A. Djurdjevac, H. Kremp), Stochastics and Partial Differential Equations: Analysis and Computations, 2024, Vol. 12. Published version.
An extension of the stochastic sewing lemma and applications to fractional stochastic calculus (with T. Matsuda), Forum of Mathematics, Sigma, 2024, Vol. 12, no. 52. Published version.
2023
Hopf Bifurcations of Moore-Greitzer PDE Model with Additive Noise (with Y.Meng, N.Sri Namachchivaya), Journal of Nonlinear Science, 2023, Vol. 33, no. 5, p.74
A Fourier Analysis Based New Look at Integration (with P. Imkeller), Annales Mathematicae Silesianae 37 (2023), no. 2, 149–168
Quantitative heat kernel estimates for diffusions with distributional drift (with W. van Zuijlen), Potential Analysis 59 (2023), 731–752 Published version.
A simple construction of the dynamical Phi-4-3 model (with A. Jagannath), Transactions of the American Mathematical Society, 2023, Vol. 376. Published version.
2022
Approximation of the Filter Equation for Multiple Timescale, Correlated, Nonlinear Systems (with R. Beeson, N.S. Namachchivaya), SIAM Journal on Mathematical Analysis, 2022, Vol. 54, no. 3. Published version.
Long-time asymptotics of the two-dimensional parabolic Anderson model with white-noise potential (with W. König, W. van Zuijlen), Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 2022 Vol. 58, no. 3. Published version.
Multidimensional SDE with distributional drift and Lévy noise (with H. Kremp), Bernoulli, 2022, Vol. 28, no.3. Published version.
One-dimensional game-theoretic differential equations (with. R. Łochowski, D. Prömel), International Journal of Approximate Reasoning, 2022, Vol. 141. Published version.
2021
C-infinity regularization of ODEs perturbed by noise (with F. Harang), Stochastics and Dynamics, 2021, Vol. 21, no. 8. Published version.
Additive functionals as rough paths (with J.-D. Deuschel and T. Orenshtein), Annals of Probability, 2021, Vol. 49, no. 3. Published version.
A rough super-Brownian motion (with T. Rosati), Annals of Probability, 2021, Vol. 49, no. 2. Published version.
2020
The infinitesimal generator of the stochastic Burgers equation (with M. Gubinelli), Probability Theory and Related Fields, 2020, Vol. 178. Published version.
A Littlewood-Paley description of modelled distributions (with J. Martin), Journal of Functional Analysis, 2020, Vol. 279. Published version.
Particle Filters with Nudging in Multiscale Chaotic Systems: With Application to the Lorenz ’96 Atmospheric Model (with H.C. Yeong, R.T. Beeson, N.S. Namachchivaya), Journal of Nonlinear Science, 2020. Published version.
Optimal investment decision under switching regimes of subsidy support (with C. Oliveira), European Journal of Operational Research, 2020, Vol. 285. Published version.
Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEP (with P. Gonçalves, M. Simon), Annales Henri Lebesgue, 2020, Vol. 3. Published version.
2019
The KPZ equation on the real line (with T. Rosati), Electronic Journal of Probability, 2019, Vol. 24. Published version.
Paracontrolled distributions on Bravais lattices and weak universality of the 2d parabolic Anderson model (with J. Martin), Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 2019, Vol. 55, no. 4. Published version.
Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity (with R. Cont), Transactions of the American Mathematical Society, Series B, 2019, Vol. 6. Published version.
2018
A superhedging approach to stochastic integration (with D. Prömel and R. Łochowski), Stochastic Processes and their Applications, 2018, Vol. 128, no. 12. Published version.
Energy solutions of KPZ are unique (with M. Gubinelli), Journal of the American Mathematical Society, 2018, Vol. 31. Published version.
An introduction to singular SPDEs (with M. Gubinelli), Stochastic Partial Differential Equations and Related Fields. In Honor of Michael Röckner, 2018. Published version.
Probabilistic approach to the stochastic Burgers equation (with M. Gubinelli), Stochastic Partial Differential Equations and Related Fields. In Honor of Michael Röckner, 2018. Published version.
2017
The Kardar–Parisi–Zhang equation as scaling limit of weakly asymmetric interacting Brownian motions (with J. Diehl and M. Gubinelli), Communications in Mathematical Physics, 2017, Vol. 354, no. 2. Published version.
Pathwise super-replication via Vovk's outer measure (with M. Beiglböck, A.M.G. Cox, M. Huesmann, D. Prömel), Finance and Stochastics, 2017, Vol. 21, no. 4. Published version.
An invariance principle for the two-dimensional parabolic Anderson model with small potential (with K. Chouk and J. Gairing), Stochastics and Partial Differential Equations: Analysis and Computations, 2017, Vol. 5, no. 4. Published version.
KPZ reloaded (with M. Gubinelli), Communications in Mathematical Physics, 2017, Vol. 349, no. 1. Published version.
2016
The Hairer–Quastel universality result at stationarity (with M. Gubinelli), RIMS Kôkyûroku Bessatsu B59, 2016.
A Fourier analytic approach to pathwise stochastic integration (with M. Gubinelli, P. Imkeller), Electronic Journal of Probability, 2016, Vol. 21, no. 2. Published version.
Pathwise stochastic integrals for model free finance (with D. Prömel), Bernoulli, 2016, Vol. 22, no. 4. Published version.
2015
Lectures on singular stochastic PDEs (with M. Gubinelli), Ensaios Matematicos, 2015, Vol. 29. Published version.
Local times for typical price paths and pathwise Tanaka formulas (with D. Prömel), Electronic Journal of Probability, 2015, Vol. 20, no. 46. Published version.
Paracontrolled distributions and singular PDEs (with M. Gubinelli, P. Imkeller), Forum of Mathematics, Pi, 2015, Vol. 3, no. 6. Published version.
The existence of dominating local martingale measures (with P. Imkeller), Finance and Stochastics, 2015, Vol. 19, no. 4. Published version.
Supermartingales as Radon-Nikodym densities and related measure extensions (with J. Ruf), Annals of Probability, 2015, Vol. 43, no. 6. Published version.
2014
Optimal nudging in particle filters (with N. Lingala, N.S. Namachchivaya, Z. Rapti, H.C. Yeong), Probabilistic Engineering Mechanics, 2014, Vol. 37. Published version.
2013
Dimensional reduction in nonlinear filtering: a homogenization approach (with P. Imkeller, N.S. Namachchivaya, H.C. Yeong), Annals of Applied Probability, 2013, Vol. 23, no. 6. Published version.
Large deviations for Hilbert space valued Wiener processes: a sequence space approach (with A. Andresen, P. Imkeller), Malliavin Calculus and Stochastic Analysis: a Festschrift in Honor of David Nualart, 2013. Published version.
2012
Particle filtering in high-dimensional chaotic systems (with N. Lingala, N.S. Namachchivaya, H.C. Yeong), Chaos, 2012, Vol. 22, no. 4. Published version.
Conditioned martingales (with J. Ruf), Electronic Communications in Probability, 2012, Vol. 17, no. 48. Published version.

Preprints

Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions (with L. Gräfner, S. Popat), submitted (2024)
Weak well-posedness of energy solutions to singular SDEs with supercritical distributional drift (with L. Gräfner) (2024)
Fractional stochastic Landau-Lifshitz Navier-Stokes equations in dimension d≥3: Existence and (non-)triviality (with R. Jin) (2024)
Rough weak solutions for singular Lévy SDEs (with H. Kremp), submitted (2023)
Rough homogenization for Langevin dynamics on fluctuating Helfrich surfaces (with A. Djurdjevac, H. Kremp), submitted (2022)
Quantitative Convergence of the Filter Solution for Multiple Timescale Nonlinear Systems with Coarse-Grain Correlated Noise (with R. Beeson, N.S. Namachchivaya), submitted (2020)

Conference Proceedings

Hairer-Quastel universality with energy solutions (with M. Gubinelli), Oberwolfach Report 24/2016. Published version.
Optimal Nudging in Particle Filters (with N. Lingala, N.S. Namachchivaya, H.C. Yeong), Procedia IUTAM, 2013, Vol. 6. Published version.
A Homogenization Approach to Multiscale Filtering (with P. Imkeller, N.S. Namachchivaya, H.C. Yeong), Procedia IUTAM, 2012, Vol. 5. Published version.
A theory of controlled distributions (with M. Gubinelli, P. Imkeller), Oberwolfach Report 41/2012. Published version.

Other

Unpublished lecture notes for a mini course on energy solutions to singular SPDEs that I taught at the summer school PDE and Randomness at the Brin Mathematics Research Center at University of Maryland in 2024.
Unpublished lecture notes for a mini course on rough analysis that I taught at the 9th Regional Summer School on Applied Mathematics in Sinaia in 2024.
Unpublished lecture notes for a course on paracontrolled distributions that I taught at MPI Leipzig in Winter 2018/19.
Unpublished lecture notes for a mini course on energy solutions to the stochastic Burgers equation that I taught at Bielefeld University in May 2018.
Unpublished lecture notes for a mini course on paracontrolled distributions and singular diffusions that I taught at the Hausdorff Center in Bonn in February 2017.
My PhD thesis.
My diploma thesis on the subject of exchangeable stochastic population models.
Unpublished Lecture notes for a mini course on backward stochastic differential equations that I taught at the University of Illinois at Urbana Champaign in November 2010.

List of Co-Authors

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Fachbereich Mathematik und Informatik

Dynamische Systeme / Stochastik

Publications and Preprints

Publications

Preprints

Conference Proceedings

Other

List of Co-Authors