13 citations · 31 across the 10 of their papers we have counts for
10 papers
Piecewise linear interpolation of noise in finite element approximations of parabolic SPDEs
Gabriel Lord, Andreas Petersson
Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of nois…
The heat modulated infinite dimensional Heston model and its numerical approximation
Fred Espen Benth, Gabriel Lord, Giulia Di Nunno +1
The HEat modulated Infinite DImensional Heston (HEIDIH) model and its numerical approximation are introduced and analyzed. This model falls into the general framework of infinite d…
SPDE bridges with observation noise and their spatial approximation
Giulia Di Nunno, Salvador Ortiz-Latorre, Andreas Petersson
This paper introduces SPDE bridges with observation noise and contains an analysis of their spatially semidiscrete approximations. The SPDEs are considered in the form of mild solu…
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…
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…
Rapid covariance-based sampling of linear SPDE approximations in the multilevel Monte Carlo method
Andreas Petersson
The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is co…
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…
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…