Aktuelle Forschungsfelder

  •     Stochastische PDEs
  •     Regularitätsstrukturen
  •     Grobe Pfade
  •     Regularisierung durch Rauschen
  •     Numerische Aspekte von Stochastischen Gleichungen
Publikationen
  1. Regularisation by Gaussian rough path lifts of fractional Brownian motions
    with K. Dareiotis and C. Ling and K. Lê
    arXiv:2412.01645
  2. Weak coupling limit of KPZ with rougher than white noise
    with F. Toninelli
    arXiv:2406.08364
  3. Higher order approximation of nonlinear SPDEs with additive space-time white noise
    with A. Djurdjevac and H. Kremp
    arXiv:2406.03058
  4. Analytically weak solutions to stochastic heat equations with spatially rough noise
    arXiv:2404.18920
  5. Quasi-generalised KPZ equation
    with Y. Bruned and U. Nadeem
    arXiv:2401.13620
  6. A central limit theorem for the Euler method for SDEs with irregular drifts
    with K. Dareiotis and K. Lê
    arXiv:2309.16339
  7. The Milstein scheme for singular SDEs with Hölder continuous drift
    with G. Lampl and C. Ling
    arXiv:2305.16004
  8. 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
  9. 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
  10. Solution theory of fractional SDEs in complete subcritical regimes
    with L. Galeati
    arXiv:2207.03475
  11. 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
  12. 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
  13. Boundary renormalisation of SPDEs
    with M. Hairer
    Comm. Partial Differential Equations (2022), doi:10.1080/03605302.2022.2109173, arXiv:2110.03656
  14. 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
  15. Regularisation by regular noise
    Stoch. PDE: Anal. Comp. (2022), doi:10.1007/s40072-022-00242-0, arXiv:2009.08418
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. A solution theory for quasilinear singular SPDEs
    with M. Hairer
    Comm. Pure Appl. Math. (2019), doi:10.1002/cpa.21816, arXiv:1712.01881
  23. Boundary regularity of stochastic PDEs
    Ann. Probab. (2019), doi:10.1214/18-AOP1272, arXiv:1705.05364
  24. Singular SPDEs in domains with boundaries
    with M. Hairer
    Probab. Theory Related Fields (2019), doi:10.1007/s00440-018-0841-1, arXiv:1702.06522
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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