26 citations · 76 across the 10 of their papers we have counts for
15 papers
Adaptive Quantile Computation for Brownian Bridge in Change-Point Analysis
Jürgen Franke, Mario Hefter, André Herzwurm +2
As an example for the fast calculation of distributional parameters of Gaussian processes, we propose a new Monte Carlo algorithm for the computation of quantiles of the supremum n…
An Adaptive Random Bit Multilevel Algorithm for SDEs
Michael B. Giles, Mario Hefter, Lukas Mayer +1
We study the approximation of expectations for solutions of stochastic differential equations and functionals on the path space by means of Monte C…
Embeddings for Infinite-Dimensional Integration and -Approximation with Increasing Smoothness
M. Gnewuch, M. Hefter, A. Hinrichs +2
We study integration and -approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, whic…
Random Bit Multilevel Algorithms for Stochastic Differential Equations
Michael B. Giles, Mario Hefter, Lukas Mayer +1
We study the approximation of expectations $\E(f(X))$ for solutions of SDEs and functionals by means of restricted Monte Carlo algorithms that m…
Lower Error Bounds for Strong Approximation of Scalar SDEs with non-Lipschitzian Coefficients
Mario Hefter, André Herzwurm, Thomas Müller-Gronbach
We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observati…
Random Bit Quadrature and Approximation of Distributions on Hilbert Spaces
Michael B. Giles, Mario Hefter, Lukas Mayer +1
We study the approximation of expectations $\E(f(X))$ for Gaussian random elements with values in a separable Hilbert space and Lipschitz continuous functionals $f \colon H…
Counterexamples to regularities for the derivative processes associated to stochastic evolution equations
Mario Hefter, Arnulf Jentzen, Ryan Kurniawan
In the recent years there has been an increased interest in studying regularity properties of the derivatives of stochastic evolution equations (SEEs) with respect to their initial…
On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes
Mario Hefter, Arnulf Jentzen
Cox-Ingersoll-Ross (CIR) processes are extensively used in state-of-the-art models for the approximative pricing of financial derivatives. In particular, CIR processes are day afte…
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…