Publications and Preprints
of Prof. Dr. Nicolas Perkowski
Publications
For the final versions please consult the journals.
- 2021
- One-dimensional game-theoretic differential equations (with. R. Łochowski, D. Prömel), to appear in International Journal of Approximate Reasoning (2021+). Published version.
- C-infinity regularization of ODEs perturbed by noise (with F. Harang), to appear in Stochastics and Dynamics (2021+). 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
- Quantitative Convergence of the Filter Solution for Multiple Timescale Nonlinear Systems with Coarse-Grain Correlated Noise (with R. Beeson, N.S. Namachchivaya), submitted (2020)
- Approximation of the Filter Equation for Multiple Timescale, Correlated, Nonlinear Systems (with R. Beeson, N.S. Namachchivaya), submitted (2020)
- Long-time asymptotics of the two-dimensional parabolic Anderson model with white-noise potential (with W. König, W. van Zuijlen), submitted (2020)
- Quantitative heat kernel estimates for diffusions with distributional drift (with W. van Zuijlen), submitted (2020)
-
Multidimensional SDE with distributional drift and Lévy noise (with H. Kremp), 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 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
- A. Andresen
- R.T. Beeson
- M. Beiglböck
- K. Chouk
- R. Cont
- A.M.G. Cox
- J.-D. Deuschel
- J. Diehl
- J. Gairing
- P. Gonçalves
- M. Gubinelli
- F. Harang
- M. Huesmann
- P. Imkeller
- W. König
- H. Kremp
- N. Lingala
- R. Łochowski
- J. Martin
- N.S. Namachchivaya
- C. Oliveira
- T. Orenshtein
- D. Prömel
- Z. Rapti
- J. Ruf
- T. Rosati
- M. Simon
- W. van Zuijlen
- H.C. Yeong