Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise
We consider the numerical approximation of a general second-order semilinear parabolic
stochastic partial differential equation driven by multiplicative and additive space–time …
stochastic partial differential equation driven by multiplicative and additive space–time …
A mild Itô formula for SPDEs
This article introduces a certain class of stochastic processes, which we suggest calling mild
Itô processes, and a new, somehow mild, Itô-type formula for such processes. Examples of …
Itô processes, and a new, somehow mild, Itô-type formula for such processes. Examples of …
Higher order pathwise numerical approximations of SPDEs with additive noise
A Jentzen - SIAM Journal on Numerical Analysis, 2011 - SIAM
In this article the pathwise numerical approximation of semilinear parabolic stochastic partial
differential equations (SPDEs) driven by additive noise is considered. A new numerical …
differential equations (SPDEs) driven by additive noise is considered. A new numerical …
Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems
C Beck, S Becker, P Cheridito, A Jentzen… - arXiv preprint arXiv …, 2020 - arxiv.org
In this article we introduce and study a deep learning based approximation algorithm for
solutions of stochastic partial differential equations (SPDEs). In the proposed approximation …
solutions of stochastic partial differential equations (SPDEs). In the proposed approximation …
Weak convergence for a stochastic exponential integrator and finite element discretization of stochastic partial differential equation with multiplicative & additive noise
A Tambue, JMT Ngnotchouye - Applied Numerical Mathematics, 2016 - Elsevier
We consider a finite element approximation of a general semi-linear stochastic partial
differential equation (SPDE) driven by space-time multiplicative and additive noise. We …
differential equation (SPDE) driven by space-time multiplicative and additive noise. We …
An exponential Wagner--Platen type scheme for SPDEs
S Becker, A Jentzen, PE Kloeden - SIAM Journal on Numerical Analysis, 2016 - SIAM
The strong numerical approximation of semilinear stochastic partial differential equations
(SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a …
(SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a …
Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme
We study the random heat partial differential equation on a bounded domain assuming that
the diffusion coefficient and the boundary conditions are random variables, and the initial …
the diffusion coefficient and the boundary conditions are random variables, and the initial …
Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations
We construct a positivity-preserving Lie--Trotter splitting scheme with finite difference
discretization in space for approximating the solutions to a class of nonlinear stochastic heat …
discretization in space for approximating the solutions to a class of nonlinear stochastic heat …
Strongly convergent error analysis for a spatially semidiscrete approximation of stochastic partial differential equations with non-globally Lipschitz continuous …
X Yang, W Zhao - Journal of Computational and Applied Mathematics, 2021 - Elsevier
We study a spatially semidiscrete approximation of nonlinear stochastic partial differential
equations (SPDEs) driven by multiplicative noise under weak assumptions on the …
equations (SPDEs) driven by multiplicative noise under weak assumptions on the …
[HTML][HTML] An exponential integrator for finite volume discretization of a reaction–advection–diffusion equation
A Tambue - Computers & Mathematics with Applications, 2016 - Elsevier
We consider the numerical approximation of a general second order semi-linear parabolic
partial differential equation. Equations of this type arise in many contexts, such as transport …
partial differential equation. Equations of this type arise in many contexts, such as transport …