17 citations · 80 across the 17 of their papers we have counts for
20 papers
Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks
Davide Gallon, Arnulf Jentzen, Felix Lindner
In this article we investigate blow up phenomena for gradient descent optimization methods in the training of artificial neural networks (ANNs). Our theoretical analysis is focused…
Stochastic aspects of crack deflection and crack path prediction in short fiber reinforced polymer matrix composites
Andreas Ricoeur, Felix Lindner, Konstantin Zarjov
Owing to the production process, short fiber reinforced composites exhibit a pronounced anisotropy of both elastic properties and crack growth resistance. In particular the latter…
Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations
Martin Hutzenthaler, Arnulf Jentzen, Felix Lindner +1
The main result of this article establishes strong convergence rates on the whole probability space for explicit space-time discrete numerical approximations for a class of stochas…
Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise
Arnulf Jentzen, Felix Lindner, Primož Pušnik
In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combina…
Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
Matteo Beccari, Martin Hutzenthaler, Arnulf Jentzen +3
The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimension…
Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noise
Sonja Cox, Arnulf Jentzen, Felix Lindner
In this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson mod…
Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions
Arnulf Jentzen, Felix Lindner, Primož Pušnik
In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform Hölder continuity in time, and strong convergence rates for a…
On the Alekseev-Gröbner formula in Banach spaces
Arnulf Jentzen, Felix Lindner, Primož Pušnik
The Alekseev-Gröbner formula is a well known tool in numerical analysis for describing the effect that a perturbation of an ordinary differential equation (ODE) has on its solution…
Malliavin regularity and weak approximation of semilinear SPDE with Lévy noise
Adam Andersson, Felix Lindner
We investigate the weak order of convergence for space-time discrete approximations of semilinear parabolic stochastic evolution equations driven by additive square-integrable Lévy…
Strong convergence of a half-explicit Euler scheme for constrained stochastic mechanical systems
Felix Lindner, Holger Stroot
This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. Such systems are described by second order stochasti…
Poisson Malliavin calculus in Hilbert space with an application to SPDE
Adam Andersson, Felix Lindner
In this paper we introduce a Hilbert space-valued Malliavin calculus for Poisson random measures. It is solely based on elementary principles from the theory of point processes and…
An -estimate for the stochastic heat equation on an angular domain in
Petru A. Cioica-Licht, Kyeong-Hun Kim, Kijung Lee +1
We prove a weighted -estimate for the stochastic convolution associated to the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain $\mat…
Weak error analysis via functional Itô calculus
Mihály Kovács, Felix Lindner
We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functi…
Stochastic fiber dynamics in a spatially semi-discrete setting
Felix Lindner, Nicole Marheineke, Holger Stroot +2
We investigate a spatially discrete surrogate model for the dynamics of a slender, elastic, inextensible fiber in turbulent flows. Deduced from a continuous space-time beam model f…
On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEs
Petru A. Cioica, Stephan Dahlke, Nicolas Döhring +6
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme…
Weak convergence of finite element approximations of linear stochastic evolution equations with additive Lévy noise
Mihály Kovács, Felix Lindner, René L. Schilling
We present an abstract framework to study weak convergence of numerical approximations of linear stochastic partial differential equations driven by additive Lévy noise. We first d…
Singular Behavior of the Solution to the Stochastic Heat Equation on a Polygonal Domain
Felix Lindner
We study the stochastic heat equation with trace class noise and zero Dirichlet boundary condition on a bounded polygonal domain O in R^2. It is shown that the solution u can be de…
On the Lq(Lp)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains
Petru A. Cioica, Kyeong-Hun Kim, Kijung Lee +1
We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains with both theoretical and…
Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains
Petru A. Cioica, Stephan Dahlke, Stefan Kinzel +4
We use the scale of Besov spaces B^α_{τ,τ}(O), α>0, 1/τ=α/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equat…
Weak order for the discretization of the stochastic heat equation driven by impulsive noise
Felix Lindner, René L. Schilling
Considering a linear parabolic stochastic partial differential equation driven by impulsive space time noise, dX_t+AX_t dt= Q^{1/2}dZ_t, X_0=x_0\in H, t\in [0,T], we approximate th…