[图书][B] Numerical methods for stochastic partial differential equations with white noise
Z Zhang, GE Karniadakis - 2017 - Springer
In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …
The numerical approximation of stochastic partial differential equations
A Jentzen, PE Kloeden - Milan Journal of Mathematics, 2009 - Springer
The numerical solution of stochastic partial differential equations (SPDEs) is at a stage of
development roughly similar to that of stochastic ordinary differential equations (SODEs) in …
development roughly similar to that of stochastic ordinary differential equations (SODEs) in …
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 …
Galerkin approximations for the stochastic Burgers equation
Existence and uniqueness for semilinear stochastic evolution equations with additive noise
by means of finite-dimensional Galerkin approximations is established and the convergence …
by means of finite-dimensional Galerkin approximations is established and the convergence …
A Milstein scheme for SPDEs
This article studies an infinite-dimensional analog of Milstein's scheme for finite-dimensional
stochastic ordinary differential equations (SODEs). The Milstein scheme is known to be …
stochastic ordinary differential equations (SODEs). The Milstein scheme is known to be …
[HTML][HTML] The exponential integrator scheme for stochastic partial differential equations: pathwise error bounds
We present an error analysis for the pathwise approximation of a general semilinear
stochastic evolution equation in d dimensions. We discretise in space by a Galerkin method …
stochastic evolution equation in d dimensions. We discretise in space by a Galerkin method …
Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients
A Jentzen - Potential Analysis, 2009 - Springer
We consider the pathwise numerical approximation of nonlinear parabolic stochastic partial
differential equations (SPDEs) driven by additive white noise under local assumptions on …
differential equations (SPDEs) driven by additive white noise under local assumptions on …
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 …
High order integrator for sampling the invariant distribution of a class of parabolic stochastic PDEs with additive space-time noise
CE Bréhier, G Vilmart - SIAM Journal on Scientific Computing, 2016 - SIAM
We introduce a time-integrator to sample with high order of accuracy the invariant
distribution for a class of semilinear stochastic PDEs (SPDEs) driven by an additive space …
distribution for a class of semilinear stochastic PDEs (SPDEs) driven by an additive space …