142 citations · 370 across the 21 of their papers we have counts for
9 papers · 1 filter
Hilbert--Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations
Mihály Kovács, Annika Lang, Andreas Petersson
Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on…
Continuity of Random Fields on Riemannian Manifolds
Annika Lang, Jürgen Potthoff, Martin Schlather +1
A theorem of the Kolmogorov--Chentsov type is proved for random fields on a Riemannian manifold.
Numerical analysis of lognormal diffusions on the sphere
Lukas Herrmann, Annika Lang, Christoph Schwab
Numerical solutions of stationary diffusion equations on the unit sphere with isotropic lognormal diffusion coefficients are considered. Hölder regularity in sense for isotro…
Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations
Annika Lang, Andreas Petersson
The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approxi…
A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes
Annika Lang
It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding…
Covariance structure of parabolic stochastic partial differential equations with multiplicative Lévy noise
Kristin Kirchner, Annika Lang, Stig Larsson
The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative Lévy n…
Kolmogorov-Chentsov theorem and differentiability of random fields on manifolds
Roman Andreev, Annika Lang
A version of the Kolmogorov-Chentsov theorem on sample differentiability and Hölder continuity of random fields on domains of cone type is proved, and the result is generalized to…
Isotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations
Annika Lang, Christoph Schwab
Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Loève expansions with respect to the spherical harmonic functions and the angular power spectrum. The s…
Covariance structure of parabolic stochastic partial differential equations
Annika Lang, Stig Larsson, Christoph Schwab
In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, te…