26 citations · 76 across the 10 of their papers we have counts for
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Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces
Mario Hefter, Arnulf Jentzen, Ryan Kurniawan
Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in…
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces
Adam Andersson, Mario Hefter, Arnulf Jentzen +1
In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear diff…
Equivalence of Weighted Anchored and ANOVA Spaces of Functions with Mixed Smoothness of Order one in
Michael Gnewuch, Mario Hefter, Aicke Hinrichs +2
We consider -weighted anchored and ANOVA spaces of functions with mixed first order partial derivatives bounded in a weighted norm with . The domain…
Embeddings of Weighted Hilbert Spaces and Applications to Multivariate and Infinite-Dimensional Integration
Michael Gnewuch, Mario Hefter, Aicke Hinrichs +1
We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to…
Strong Convergence Rates for Cox-Ingersoll-Ross Processes - Full Parameter Range
Mario Hefter, André Herzwurm
We study strong (pathwise) approximation of Cox-Ingersoll-Ross processes. We propose a Milstein-type scheme that is suitably truncated close to zero, where the diffusion coefficien…
Optimal Strong Approximation of the One-dimensional Squared {B}essel Process
Mario Hefter, André Herzwurm
We consider the one-dimensional squared Bessel process given by the stochastic differential equation (SDE) \begin{align*} dX_t = 1\,dt + 2\sqrt{X_t}\,dW_t, \quad X_0=x_0, \quad t\i…
Adaptive Approximation of the Minimum of Brownian Motion
James M. Calvin, Mario Hefter, André Herzwurm
We study the error in approximating the minimum of a Brownian motion on the unit interval based on finitely many point evaluations. We construct an algorithm that adaptively choose…