PSD and Cross-PSD of Responses of Seven Classes of Fractional Vibrations Driven by fGn, fBm, Fractional OU Process, and von Kármán Process
M Li - Symmetry, 2024 - mdpi.com
This paper gives its contributions in four stages. First, we propose the analytical expressions
of power spectrum density (PSD) responses and cross-PSD responses to seven classes of …
of power spectrum density (PSD) responses and cross-PSD responses to seven classes of …
Stochastic transport with Lévy noise fully discrete numerical approximation
A Stein, A Barth - Mathematics and Computers in Simulation, 2025 - Elsevier
Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread
applications in the natural and engineering sciences. However, the traditional Gaussian …
applications in the natural and engineering sciences. However, the traditional Gaussian …
[HTML][HTML] Optimal strong convergence rates of numerical methods for semilinear parabolic SPDE driven by Gaussian noise and Poisson random measure
This paper deals with the numerical approximation of semilinear parabolic stochastic partial
differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random …
differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random …
An Antithetic Multilevel Monte Carlo-Milstein Scheme for Stochastic Partial Differential Equations
AL Haji-Al, A Stein - arXiv preprint arXiv:2307.14169, 2023 - arxiv.org
We present a novel multilevel Monte Carlo approach for estimating quantities of interest for
stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and …
stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and …
Finite element methods and their error analysis for SPDEs driven by Gaussian and non-Gaussian noises
X Yang, W Zhao - Applied Mathematics and Computation, 2018 - Elsevier
In this paper, we investigate the mean square error of numerical methods for SPDEs driven
by Gaussian and non-Gaussian noises. The Gaussian noise considered here is a Hilbert …
by Gaussian and non-Gaussian noises. The Gaussian noise considered here is a Hilbert …
Malliavin regularity and weak approximation of semilinear SPDE with L\'evy noise
A Andersson, F Lindner - arXiv preprint arXiv:1808.08574, 2018 - arxiv.org
We investigate the weak order of convergence for space-time discrete approximations of
semilinear parabolic stochastic evolution equations driven by additive square-integrable …
semilinear parabolic stochastic evolution equations driven by additive square-integrable …
[图书][B] Multiscale methods for evolution problems
P Ljung - 2023 - search.proquest.com
In this thesis we develop and analyze generalized finite element methods for time-
dependent partial differential equations (PDEs). The focus lies on equations with rapidly …
dependent partial differential equations (PDEs). The focus lies on equations with rapidly …
Stochastic Transport with L\'evy Noise--Fully Discrete Numerical Approximation
Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread
applications in the natural and engineering sciences. However, the traditional Gaussian …
applications in the natural and engineering sciences. However, the traditional Gaussian …
Weak convergence rates for numerical approximations of parabolic stochastic partial differential equations with non-additive noise
R Kurniawan - 2018 - research-collection.ethz.ch
Strong convergence rates for numerical approximations of stochastic partial differential
equations (SPDEs) with smooth and regular nonlinearities are well understood in the …
equations (SPDEs) with smooth and regular nonlinearities are well understood in the …
Uncertainty quantification with Lévy-type random fields
A Stein - 2020 - elib.uni-stuttgart.de
A countless number of models in the natural sciences, engineering and economics are
based on partial differential equations (PDEs). Due to insufficient data or measurement …
based on partial differential equations (PDEs). Due to insufficient data or measurement …