Preprints 2019

Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

Project: B1

Published: BIT Numerical Mathematics 60, no. 4 (2020), 1057–1073

Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations

Project: B1

Published: Stochastic Partial Differential Equations. Analysis and Computations 11, no. 1 (2023), 211-268

Density bounds for solutions to differential equations driven by Gaussian rough paths

Project: B1

Published: Journal of Theoretical Probability 33, no. 2 (2020), 611–648

Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise

Project: B1

Published: Journal de Mathématiques Pures et Appliquées. Neuvième Série 9, no. 148 (2021), 221-226

Nonlinear diffusion equations with nonlinear gradient noise

Project: B1

Published: Electronic Journal of Probability 25, no. 35 (2020), 43 pp.

Optimal regularity in time and space for the porous medium equation

Project: B1

To appear: Analysis and PDE (2020)

Convergence rates for the stochastic gradient descent method for non-convex objective functions

Project: B1

Published: Journal of Machine Learning Research 21, no. 136 (2020), 48 pp.

The stochastic thin-film equation: existence of nonnegative martingale solutions

Project: B1

Published: Stochastic Processes and their Applications 130, no. 12 (2020), 7260–7302

Schauder Theorems for a class of (pseudo-)differential operators on finite and infinite dimensional state spaces

Project: B1

Published: Journal of the London Mathematical Society 104, no. 2 (2021), 492-540

Notes: https://doi.org/10.1112/jlms.12436

Game Options under Knightian Uncertainty in Discrete Time

Project: C3

Convergent numerical approximation of the stochastic total variation flow

Project: B1, B3

Published: Stochastics and Partial Differential Equations: Analysis and Computations 9, no. 2 (2021), 437–471

Renormalisation of pair correlations and their Fourier transforms for primitive block substitutions

Project: A6

Published: Substitution and Tiling Dynamics: Introduction to Self-inducing Structures (2020), 359–395

$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations

Project: A3

Published: Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal 195, no. 111730 (2020), 28

Upper envelopes of families of Feller semigroups and viscosity solutions to a class of nonlinear Cauchy problems

Project: A5, C5

Published: SIAM Journal of Control and Optimization 59, no. 6 (2021), 4400-4428

Notes: https://doi.org/10.1137/20M1314823

Numerical Approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit

Project: B3

Published: Numerische Mathematik 147, no. 3 (2021), 505-551

Averaging principle for slow-fast stochastic differential equations with time dependent locally Lipschitz coefficients

Project: B1

Published: Journal of Differential Equations 268 (2019), 2910–2948

On convergence to stationary distributions for solutions of nonlinear Fokker–Planck–Kolmogorov equations

Project: A5

Published: Journal of Mathematical Sciences 1 (2019), 69–84

Families of two-dimensional Coulomb gases on anellipse: correlation functions and universality

Project: B5

Published: Journal of Physics A: Mathematical and Theoretical 53 (2020), 075201: 1–36

Gegenbauer and other planar orthogonal polynomials on an ellipse in the complex plane

Project: B5

To appear: Constructive Approximation (2020)

Universal bounds and monotonicity properties of ratios of Hermite and parabolic cylinder functions

Project: C4

Published: Proceedings of the American Mathematical Society 148 (2020), 2149–2155