Welcome to my website. I am an Associate Professor at TU Wien in the Institute of Analysis and Scientific Computing (ASC). From March 2024 I am honored to be supported by an ERC Starting Grant.
You can reach me at mate.gerencser*at*tuwien.ac.at
My research interest lies in stochastic analysis: stochastic PDEs, regularity structures, rough paths, regularisation by noise, and numerical aspects of stochastic equations.
Publications
- Quasi-generalised KPZ equation
with Y. Bruned and U. Nadeem
arXiv:2401.13620 - A central limit theorem for the Euler method for SDEs with irregular drifts
with K. Dareiotis and K. Lê
arXiv:2309.16339 - The Milstein scheme for singular SDEs with Hölder continuous drift
with G. Lampl and C. Ling
arXiv:2305.16004 - Strong convergence of parabolic rate 1 of discretisations of stochastic Allen-Cahn-type equations
with H. Singh
Trans. AMS (2023+), to appear, arXiv:2209.09222 - Path-by-path regularisation through multiplicative noise in rough, Young, and ordinary differential equations
with K. Dareiotis
Ann. Probab. (2024+), to appear, arXiv:2207.03476 - Solution theory of fractional SDEs in complete subcritical regimes
with L. Galeati
arXiv:2207.03475 - Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Levy noise
with O. Butkovsky and K. Dareiotis
arXiv:2204.12926 - Optimal rate of convergence for approximations of SPDEs with non-regular drift
with O. Butkovsky and K. Dareiotis
SIAM J. Numer. Anal. (2023), doi:10.1137/21M1454213, arXiv:2110.06148 - Boundary renormalisation of SPDEs
with M. Hairer
Comm. Partial Differential Equations (2022), doi:10.1080/03605302.2022.2109173, arXiv:2110.03656 - Quantifying a convergence theorem of Gyöngy and Krylov
with K. Dareiotis and K. Lê
Annals of Applied Probability (2023), doi:10.1214/22-AAP1867 arXiv:2101.12185 - Regularisation by regular noise
Stoch. PDE: Anal. Comp. (2022), doi:10.1007/s40072-022-00242-0, arXiv:2009.08418 - Singular paths spaces and applications
with C. Bellingeri and P. K. Friz
Stoch. Anal. Appl. (2021), doi:10.1080/07362994.2021.1988641, arXiv:2003.03352 - Porous media equations with multiplicative space-time white noise
with K. Dareiotis and B. Gess
Ann. Inst. H. Poincarée Probab. Statist (2021), doi:10.1214/20-AIHP1139, arXiv:2002.12924 - Approximation of SDEs - a stochastic sewing approach
with O. Butkovsky and K. Dareiotis
Probab. Theory Related Fields (2021), doi:10.1007/s00440-021-01080-2, arXiv:1909.07961 - Nondivergence form quasilinear heat equations driven by space-time white noise
Ann. Inst. H. Poincaré Anal. Non Linéaire (2020), doi:10.1016/j.anihpc.2020.01.003, arXiv:1902.07635 - On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift
with K. Dareiotis
Electron. J. Probab. (2020), doi:10.1214/20-EJP479, arXiv:1812.04583 - Entropy solutions for stochastic porous medium equations
with K. Dareiotis and B. Gess
J. Differential Equations (2019), doi:10.1016/j.jde.2018.09.012, arXiv:1803.06953 - A solution theory for quasilinear singular SPDEs
with M. Hairer
Comm. Pure Appl. Math. (2019), doi:10.1002/cpa.21816, arXiv:1712.01881 - Boundary regularity of stochastic PDEs
Ann. Probab. (2019), doi:10.1214/18-AOP1272, arXiv:1705.05364 - Singular SPDEs in domains with boundaries
with M. Hairer
Probab. Theory Related Fields (2019), doi:10.1007/s00440-018-0841-1, arXiv:1702.06522 - On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions
with A. Jentzen and D. Salimova
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. (2017) doi:10.1098/rspa.2017.0104, arXiv:1702.03229 - A Feynman-Kac formula for stochastic Dirichlet problems
with I. Gyöngy
Stochastic Process. Appl. (2019) doi:10.1016/j.spa.2018.04.003, arXiv:1611.04177 - Localization errors in solving stochastic partial differential equations in the whole space
with I. Gyöngy
Math. Comp. (2017), doi:10.1090/mcom/3201, arXiv:1508.05535 - Local L∞-estimates, weak Harnack inequality,
and stochastic continuity of solutions of SPDEs
with K. Dareiotis
J. Differential Equations (2016), doi:10.1016/j.jde.2016.09.038, arXiv:1503.04472 - On the solvability of degenerate stochastic partial differential equations in Sobolev spaces
with I. Gyöngy and N. V. Krylov
Stoch. PDE: Anal. Comp. (2015), doi:10.1007/s40072-014-0042-6, arXiv:1404.4401 - On the boundedness of solutions of SPDEs
with K. Dareiotis
Stoch. PDE: Anal. Comp. (2015), doi:10.1007/s40072-014-0043-5, arXiv:1312.3843 - Finite difference schemes for stochastic partial differential equations in Sobolev spaces
with I. Gyöngy
Appl. Math. Optim. (2015), doi:10.1007/s00245-014-9272-2, arXiv:1308:4614
Teaching
I am currently teaching the courses Applied Mathematics Foundations and Stochastic differential equations and their numerics at TU Wien (23/24 Winter Semester). Detailed information to be found on TISS & TUWEL.
For Bahelor/Master thesis projects, please inquire by e-mail.
Past teaching (TU Wien)- Numerics of PDEs 22/23 SS
- Applied Mathematics Foundations 22/23 WS
- Stochastic PDEs 20/21, 21/22 SS
- Stochastic differential equations and their numerics 20/21, 21/22 WS
Projects
I am PI of the ERC StG project 101117125 Stochastic PDEs and Renormalisation, the FWF START project STA 119, and the FWF Stand-Alone project P 34992 Regularisation by noise in discrete and continuous systems.