80 citations · 225 across the 12 of their papers we have counts for
13 papers
Convergence in Hölder norms for Markovian approximations of stochastic Volterra equations
Noé Corneille, Kristin Kirchner, Pietro Pezzoli Frigerio
We bound the difference between two stochastic Volterra processes with identical Lipschitz coefficients but different kernels. For non-convolution kernels, we establish estimates i…
Optimized multilevel Monte Carlo methods in Banach spaces
Kristin Kirchner, Fabio Nobile, Christoph Schwab +1
We present a theoretical and numerical analysis of Monte Carlo methods for the estimation of statistical moments of random variables taking values in a Banach sp…
Multiple and weak Markov properties in Hilbert spaces with applications to fractional stochastic evolution equations
Kristin Kirchner, Joshua Willems
We define various higher-order Markov properties for stochastic processes , indexed by an interval and taking values in…
Monte Carlo convergence rates for th moments in Banach spaces
Kristin Kirchner, Christoph Schwab
We formulate standard and multilevel Monte Carlo methods for the th moment of a Banach space valued random variable , interpreted as…
Regularity theory for a new class of fractional parabolic stochastic evolution equations
Kristin Kirchner, Joshua Willems
A new class of fractional-order stochastic evolution equations of the form , , , is introduced, where genera…
Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction
Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner +1
Centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds are determined by their covariance…
Equivalence of measures and asymptotically optimal linear prediction for Gaussian random fields with fractional-order covariance operators
David Bolin, Kristin Kirchner
We consider Gaussian measures on a separable Hilbert space, with fractional-order covariance operators resp. , and derive necessary an…
Necessary and sufficient conditions for asymptotically optimal linear prediction of random fields on compact metric spaces
Kristin Kirchner, David Bolin
Optimal linear prediction (aka. kriging) of a random field indexed by a compact metric space can be obtained if the mea…
Regularity and convergence analysis in Sobolev and Hölder spaces for generalized Whittle-Matérn fields
Sonja G. Cox, Kristin Kirchner
We analyze several Galerkin approximations of a Gaussian random field indexed by a Euclidean domain $\mathcal{D}\subset\mathbb{R}…
Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise
David Bolin, Kristin Kirchner, Mihály Kovács
The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential oper…
The rational SPDE approach for Gaussian random fields with general smoothness
David Bolin, Kristin Kirchner
A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the…
Numerical solution of fractional elliptic stochastic PDEs with spatial white noise
David Bolin, Kristin Kirchner, Mihály Kovács
The numerical approximation of solutions to stochastic partial differential equations with additive spatial white noise on bounded domains in is considered. The diff…
Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs
Kristin Kirchner
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic e…