Journal: Stochastics and Partial Differential Equations: Analysis and Computations

Abbreviation

Stoch PDE: Anal Comp

Publisher

Springer

Journal Volumes

ISSN

2194-0401
2194-041X

Description

Filters

2018 - 201922020 - 20254
Reset filters

Search Results

Publications 1 - 6 of 6
  • Multilevel Monte Carlo  FEM  for elliptic PDEs with Besov random tree priors
    Item type: Journal Article
    Schwab, Christoph; Stein, Andreas (2024)
    Stochastics and Partial Differential Equations: Analysis and Computations
  • Exponential moments for numerical approximations of stochastic partial differential equations
    Item type: Journal Article
    Jentzen, Arnulf; Pušnik, Primož (2018)
    Stochastics and Partial Differential Equations: Analysis and Computations
  • Stochastic analysis with modelled distributions
    Item type: Journal Article
    Liu, Chong; Prömel, David J.; Teichmann, Josef (2021)
    Stochastics and Partial Differential Equations: Analysis and Computations
    Using a Besov topology on spaces of modelled distributions in the framework of Hairer’s regularity structures, we prove the reconstruction theorem on these Besov spaces with negative regularity. The Besov spaces of modelled distributions are shown to be UMD Banach spaces and of martingale type 2. As a consequence, this gives access to a rich stochastic integration theory and to existence and uniqueness results for mild solutions of semilinear stochastic partial differential equations in these spaces of modelled distributions and for distribution-valued SDEs. Furthermore, we provide a Fubini type theorem allowing to interchange the order of stochastic integration and reconstruction.
  • Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
    Item type: Journal Article
    Becker, Sebastian; Gess, Benjamin; Jentzen, Arnulf; et al. (2023)
    Stochastics and Partial Differential Equations: Analysis and Computations
    Strong convergence rates for fuly discrete numerical approximations of space-time white noise driven SPDEs with superlinearly growing nonlinearities, such as the stochastic Allen-Cahn equation with space-time white noise, are shown. The obtained strong rates of convergence are essentially sharp.
  • Counterexamples to regularities for the derivative processes associated to stochastic evolution equations
    Item type: Journal Article
    Hefter, Mario; Jentzen, Arnulf; Kurniawan, Ryan (2025)
    Stochastics and Partial Differential Equations: Analysis and Computations
    In the recent years there has been an increased interest in studying regularity properties of the derivatives of semilinear parabolic stochastic evolution equations (SEEs) with respect to their initial values. In particular, in the scientific literature it has been shown for every natural number n∈N that if the nonlinear drift coefficient and the nonlinear diffusion coefficient of the considered SEE are n-times continuously Fréchet differentiable, then the solution of the considered SEE is also n-times continuously Fréchet differentiable with respect to its initial value and the corresponding derivative processes satisfy a suitable regularity property in the sense that the n-th derivative process can be extended continuously to n-linear operators on negative Sobolev-type spaces with regularity parameters δ1,δ2,…,δn∈[0,∞) provided that the condition ∑i=1nδi<12 is satisfied. The main contribution of this paper is to reveal that this condition can essentially not be relaxed.
  • Numerical analysis of lognormal diffusions on the sphere
    Item type: Journal Article
    Herrmann, Lukas; Lang, Annika; Schwab, Christoph (2018)
    Stochastics and Partial Differential Equations: Analysis and Computations
Publications 1 - 6 of 6