26 citations · 76 across the 10 of their papers we have counts for
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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…
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…
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…