142 citations · 370 across the 21 of their papers we have counts for
21 papers
Euler-Maruyama approximations of the stochastic heat equation on the sphere
Annika Lang, Ioanna Motschan-Armen
The stochastic heat equation on the sphere driven by additive isotropic Wiener noise is approximated by a spectral method in space and forward and backward Euler-Maruyama schemes i…
Localized orthogonal decomposition for a multiscale parabolic stochastic partial differential equation
Annika Lang, Per Ljung, Axel Målqvist
A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localiz…
Approximation of SPDE covariance operators by finite elements: A semigroup approach
Mihály Kovács, Annika Lang, Andreas Petersson
The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the sem…
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…
Galerkin--Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds
Annika Lang, Mike Pereira
A new numerical approximation method for a class of Gaussian random fields on compact connected oriented Riemannian manifolds is introduced. This class of random fields is characte…
Numerical approximation and simulation of the stochastic wave equation on the sphere
David Cohen, Annika Lang
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical scheme…
Surface finite element approximation of spherical Whittle--Matérn Gaussian random fields
Erik Jansson, Mihály Kovács, Annika Lang
Spherical Whittle--Matérn Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done w…
Finite element approximation of Lyapunov equations related to parabolic stochastic PDEs
Adam Andersson, Annika Lang, Andreas Petersson +1
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicat…
Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise
Mihály Kovács, Annika Lang, Andreas Petersson
We consider the numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise. For the spatial approximation we consider a standard…
Drift-preserving numerical integrators for stochastic Hamiltonian systems
Chuchu Chen, David Cohen, Raffaele D'Ambrosio +1
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the…
Fast generation of isotropic Gaussian random fields on the sphere
Peter E. Creasey, Annika Lang
The efficient simulation of isotropic Gaussian random fields on the unit sphere is a task encountered frequently in numerical applications. A fast algorithm based on Markov propert…
Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions
Annika Lang, Andreas Petersson, Andreas Thalhammer
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for appro…
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…
Fast simulation of Gaussian random fields
Annika Lang, Jürgen Potthoff
Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the al…