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## On the discretization in time of parabolic stochastic partial differential equations

ESAIM: M2AN, 35 6 (2001) 1055-1078
Published online: 2002-04-15

## Regularity of the Mild Solution of a Parabolic Equation with Stochastic Measure

I. M. Bodnarchuk
Ukrainian Mathematical Journal 69 (1) 1 (2017)
DOI: 10.1007/s11253-017-1344-4

## On the Rate of Convergence of the 2-D Stochastic Leray- $$\alpha$$ α Model to the 2-D Stochastic Navier–Stokes Equations with Multiplicative Noise

Hakima Bessaih and Paul André Razafimandimby
Applied Mathematics & Optimization 74 (1) 1 (2016)
DOI: 10.1007/s00245-015-9303-7

## Finite Element Approximation of Stochastic Partial Differential Equations driven by Poisson Random Measures of Jump Type

Erika Hausenblas
SIAM Journal on Numerical Analysis 46 (1) 437 (2008)
DOI: 10.1137/050654141

## Discretization and Simulation of the Zakai Equation

Emmanuel Gobet, Gilles Page?s, Huye^n Pham and Jacques Printems
SIAM Journal on Numerical Analysis 44 (6) 2505 (2006)
DOI: 10.1137/050623140

## Higher Order Pathwise Numerical Approximations of SPDEs with Additive Noise

Arnulf Jentzen
SIAM Journal on Numerical Analysis 49 (2) 642 (2011)
DOI: 10.1137/080740714

## Monte Carlo and Quasi-Monte Carlo Methods 2012

Mihály Kovács, Stig Larsson and Karsten Urban
Springer Proceedings in Mathematics & Statistics, Monte Carlo and Quasi-Monte Carlo Methods 2012 65 481 (2013)
DOI: 10.1007/978-3-642-41095-6_24

## Numerical Methods for Stochastic Partial Differential Equations with White Noise

Zhongqiang Zhang and George Em Karniadakis
Applied Mathematical Sciences, Numerical Methods for Stochastic Partial Differential Equations with White Noise 196 53 (2017)
DOI: 10.1007/978-3-319-57511-7_3

## On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients

Martin Hutzenthaler and Arnulf Jentzen
The Annals of Probability 48 (1) (2020)
DOI: 10.1214/19-AOP1345

## Strong Convergence Analysis of the Stochastic Exponential Rosenbrock Scheme for the Finite Element Discretization of Semilinear SPDEs Driven by Multiplicative and Additive Noise

Jean Daniel Mukam and Antoine Tambue
Journal of Scientific Computing (2017)
DOI: 10.1007/s10915-017-0475-y

## Numerical methods for stochastic partial differential equations with multiple scales

A. Abdulle and G.A. Pavliotis
Journal of Computational Physics 231 (6) 2482 (2012)
DOI: 10.1016/j.jcp.2011.11.039

## On the Backward Euler Approximation of the Stochastic Allen-Cahn Equation

Mihály Kovács, Stig Larsson and Fredrik Lindgren
Journal of Applied Probability 52 (02) 323 (2015)
DOI: 10.1017/S0021900200012493

## Order of Convergence of Splitting Schemes for Both Deterministic and Stochastic Nonlinear Schrödinger Equations

Jie Liu
SIAM Journal on Numerical Analysis 51 (4) 1911 (2013)
DOI: 10.1137/12088416X

## Domain decomposition strategies for the stochastic heat equation

Erich Carelli, Alexander Müller and Andreas Prohl
International Journal of Computer Mathematics 89 (18) 2517 (2012)
DOI: 10.1080/00207160.2012.720977

## Nonconforming finite element method for stochastic Stokes equations

Xiaoyuan Yang and Ruisheng Qi
Applied Mathematical Modelling 37 (8) 6110 (2013)
DOI: 10.1016/j.apm.2012.12.005

## Finite element approximations for a linear fourth-order parabolic SPDE in two and three space dimensions with additive space–time white noise

Georgios T. Kossioris and Georgios E. Zouraris
Applied Numerical Mathematics 67 243 (2013)
DOI: 10.1016/j.apnum.2012.01.003

## Noise-induced oscillations in an actively mode-locked laser

Kelly Black and John B. Geddes
Computers & Mathematics with Applications 60 (1) 1 (2010)
DOI: 10.1016/j.camwa.2010.04.016

## On implicit and explicit discretization schemes for parabolic SPDEs in any dimension

Annie Millet and Pierre-Luc Morien
Stochastic Processes and their Applications 115 (7) 1073 (2005)
DOI: 10.1016/j.spa.2005.02.004

## A Hybrid Sparse-Grid Approach for Nonlinear Filtering Problems Based on Adaptive-Domain of the Zakai Equation Approximations

Feng Bao, Yanzhao Cao, Clayton Webster and Guannan Zhang
SIAM/ASA Journal on Uncertainty Quantification 2 (1) 784 (2014)
DOI: 10.1137/140952910

## Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise

Georgios T. Kossioris and Georgios E. Zouraris
ESAIM: Mathematical Modelling and Numerical Analysis 44 (2) 289 (2010)
DOI: 10.1051/m2an/2010003

## Pathwise Hölder convergence of the implicit-linear Euler scheme for semi-linear SPDEs with multiplicative noise

Sonja Cox and Jan van Neerven
Numerische Mathematik 125 (2) 259 (2013)
DOI: 10.1007/s00211-013-0538-4

## Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs

W. W. Mohammed, M. A. Sohaly, A. H. El-Bassiouny and K. A. Elnagar
American Journal of Computational Mathematics 04 (04) 280 (2014)
DOI: 10.4236/ajcm.2014.44024

## Strong convergence rates of the linear implicit Euler method for the finite element discretization of SPDEs with additive noise

Xiaojie Wang
IMA Journal of Numerical Analysis drw016 (2016)
DOI: 10.1093/imanum/drw016

## Splitting up method for the 2D stochastic Navier–Stokes equations

H. Bessaih, Z. Brzeźniak and A. Millet
Stochastic Partial Differential Equations: Analysis and Computations 2 (4) 433 (2014)
DOI: 10.1007/s40072-014-0041-7

## An Exponential Integrator Scheme for Time Discretization of Nonlinear Stochastic Wave Equation

Xiaojie Wang
Journal of Scientific Computing 64 (1) 234 (2015)
DOI: 10.1007/s10915-014-9931-0

## On the Convergence Analysis of the Inexact Linearly Implicit Euler Scheme for a Class of Stochastic Partial Differential Equations

P. A. Cioica, S. Dahlke, N. Döhring, et al.
Potential Analysis 44 (3) 473 (2016)
DOI: 10.1007/s11118-015-9510-5

## Strong $L^2$ convergence of time numerical schemes for the stochastic two-dimensional Navier–Stokes equations

Hakima Bessaih and Annie Millet
IMA Journal of Numerical Analysis 39 (4) 2135 (2019)
DOI: 10.1093/imanum/dry058

## A Simplified Milstein Scheme for SPDEs with Multiplicative Noise

B. Ghayebi and S. M. Hosseini
Abstract and Applied Analysis 2014 1 (2014)
DOI: 10.1155/2014/140849

## Asymptotics for a generalized Cahn-Hilliard equation with forcing terms

Dimitra C. Antonopoulou, Georgia D Karali and Georgios T. Kossioris
Discrete and Continuous Dynamical Systems 30 (4) 1037 (2011)
DOI: 10.3934/dcds.2011.30.1037

## Numerical solution of stochastic partial differential equations using a collocation method

Minoo Kamrani
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 96 (1) 106 (2016)
DOI: 10.1002/zamm.201400080

## Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise

Sonja Cox and Erika Hausenblas
International Journal of Computer Mathematics 89 (18) 2460 (2012)
DOI: 10.1080/00207160.2012.737460

## Numerical approximation of multiplicative SPDEs

I. A. Adamu and G. J. Lord
International Journal of Computer Mathematics 89 (18) 2603 (2012)
DOI: 10.1080/00207160.2012.735664

## Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise

Georgios E. Zouraris and Georgios T. Kossioris
Discrete and Continuous Dynamical Systems - Series B 18 (7) 1845 (2013)
DOI: 10.3934/dcdsb.2013.18.1845

## Optimal Strong Rates of Convergence for a Space-Time Discretization of the Stochastic Allen–Cahn Equation with Multiplicative Noise

Ananta K. Majee and Andreas Prohl
Computational Methods in Applied Mathematics 18 (2) 297 (2018)
DOI: 10.1515/cmam-2017-0023

## A fully discrete approximation of the one-dimensional stochastic wave equation

David Cohen and Lluís Quer-Sardanyons
IMA Journal of Numerical Analysis drv006 (2015)
DOI: 10.1093/imanum/drv006

## Weak convergence analysis of the linear implicit Euler method for semilinear stochastic partial differential equations with additive noise

Xiaojie Wang and Siqing Gan
Journal of Mathematical Analysis and Applications 398 (1) 151 (2013)
DOI: 10.1016/j.jmaa.2012.08.038

## Geometric Partial Differential Equations - Part I

Qiang Du and Xiaobing Feng
Handbook of Numerical Analysis, Geometric Partial Differential Equations - Part I 21 425 (2020)
DOI: 10.1016/bs.hna.2019.05.001

## Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces

Hakima Bessaih, Erika Hausenblas, Tsiry Avisoa Randrianasolo and Paul André Razafimandimby
Journal of Computational and Applied Mathematics 343 250 (2018)
DOI: 10.1016/j.cam.2018.04.067

## Numerical Solution of Stochastic Generalized Fractional Diffusion Equation by Finite Difference Method

Mathematical and Computational Applications 23 (4) 53 (2018)
DOI: 10.3390/mca23040053

## Probability and Pathwise Order of Convergence of a Semidiscrete Scheme for the Stochastic Manakov Equation

Maxime Gazeau
SIAM Journal on Numerical Analysis 52 (1) 533 (2014)
DOI: 10.1137/13090924X

## Implicit Euler method for numerical solution of nonlinear stochastic partial differential equations with multiplicative trace class noise

Minoo Kamrani, S. Mohammad Hosseini and Erika Hausenblas
Mathematical Methods in the Applied Sciences 41 (13) 4986 (2018)
DOI: 10.1002/mma.4946

## Rates of Convergence for Discretizations of the Stochastic Incompressible Navier--Stokes Equations

Erich Carelli and Andreas Prohl
SIAM Journal on Numerical Analysis 50 (5) 2467 (2012)
DOI: 10.1137/110845008

## Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear non-autonomous SPDEs driven by multiplicative or additive noise

Jean Daniel Mukam and Antoine Tambue
Applied Numerical Mathematics (2019)
DOI: 10.1016/j.apnum.2019.08.009

## Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions

Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen, Jan van Neerven and Timo Welti
IMA Journal of Numerical Analysis 41 (1) 493 (2021)
DOI: 10.1093/imanum/drz063

## Time-discretization of stochastic 2-D Navier–Stokes equations with a penalty-projection method

Erika Hausenblas and Tsiry A. Randrianasolo
Numerische Mathematik 143 (2) 339 (2019)
DOI: 10.1007/s00211-019-01057-3

## Error estimates of finite element methods for fractional stochastic Navier–Stokes equations

Xiaocui Li and Xiaoyuan Yang
Journal of Inequalities and Applications 2018 (1) (2018)
DOI: 10.1186/s13660-018-1880-y

## Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear SPDEs driven by multiplicative or additive noise

Antoine Tambue and Jean Daniel Mukam
Applied Mathematics and Computation 346 23 (2019)
DOI: 10.1016/j.amc.2018.09.073

## Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation

Charles-Edouard Bréhier, Jianbo Cui and Jialin Hong
IMA Journal of Numerical Analysis 39 (4) 2096 (2019)
DOI: 10.1093/imanum/dry052

## Strong Convergence of a Fully Discrete Finite Element Approximation of the Stochastic Cahn--Hilliard Equation

Daisuke Furihata, Mihály Kovács, Stig Larsson and Fredrik Lindgren
SIAM Journal on Numerical Analysis 56 (2) 708 (2018)
DOI: 10.1137/17M1121627

## Crank--Nicolson Finite Element Approximations for a Linear Stochastic Fourth Order Equation with Additive Space-Time White Noise

Georgios E. Zouraris
SIAM Journal on Numerical Analysis 56 (2) 838 (2018)
DOI: 10.1137/15M1053098

## Space Semi-Discretisations for a Stochastic Wave Equation

Lluís Quer-Sardanyons and Marta Sanz-Solé
Potential Analysis 24 (4) 303 (2006)
DOI: 10.1007/s11118-005-9002-0

## A numerical approximation of parabolic stochastic partial differential equations driven by a Poisson random measure

Erika Hausenblas and Iuliana Marchis
BIT Numerical Mathematics 46 (4) 773 (2006)
DOI: 10.1007/s10543-006-0099-3

## Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise

Boris Baeumer, Matthias Geissert and Mihály Kovács
Journal of Differential Equations 258 (2) 535 (2015)
DOI: 10.1016/j.jde.2014.09.020

## Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise

Electronic Journal of Probability 17 (none) (2012)
DOI: 10.1214/EJP.v17-2240

## From Stochastic Calculus to Mathematical Finance

Aureli Alabert and István Gyongy
From Stochastic Calculus to Mathematical Finance 1 (2006)
DOI: 10.1007/978-3-540-30788-4_1

## Difference Approximation of Stochastic Elastic Equation Driven by Infinite Dimensional Noise

Yinghan Zhang, Xiaoyuan Yang and Ruisheng Qi
Numerical Mathematics: Theory, Methods and Applications 9 (1) 123 (2016)
DOI: 10.4208/nmtma.2015.y14002

## On the Backward Euler Approximation of the Stochastic Allen-Cahn Equation

Mihály Kovács, Stig Larsson and Fredrik Lindgren
Journal of Applied Probability 52 (2) 323 (2015)
DOI: 10.1239/jap/1437658601

## An Implicit Algorithm of Solving Nonlinear Filtering Problems

Feng Bao, Yanzhao Cao and Xiaoying Han
Communications in Computational Physics 16 (2) 382 (2014)
DOI: 10.4208/cicp.180313.130214a

## Fractional stochastic Burgers‐type equation in Hölder space—Wellposedness and approximations

Zineb Arab and Latifa Debbi
Mathematical Methods in the Applied Sciences 44 (1) 705 (2021)
DOI: 10.1002/mma.6776

## Stochastic Analysis and Related Topics

Zdzisław Brzeźniak and Annie Millet
Springer Proceedings in Mathematics & Statistics, Stochastic Analysis and Related Topics 22 57 (2012)
DOI: 10.1007/978-3-642-29982-7_3

## A fully discrete approximation of the one-dimensional stochastic heat equation

Rikard Anton, David Cohen and Lluis Quer-Sardanyons
IMA Journal of Numerical Analysis 40 (1) 247 (2020)
DOI: 10.1093/imanum/dry060

## Strong convergence of a stochastic Rosenbrock-type scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise

Jean Daniel Mukam and Antoine Tambue
Stochastic Processes and their Applications 130 (8) 4968 (2020)
DOI: 10.1016/j.spa.2020.02.008

## Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

Primož Pušnik and Arnulf Jentzen
IMA Journal of Numerical Analysis 40 (2) 1005 (2020)
DOI: 10.1093/imanum/drz009

## An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation

Xiaojie Wang
Stochastic Processes and their Applications 130 (10) 6271 (2020)
DOI: 10.1016/j.spa.2020.05.011

## Spectral collocation method for stochastic partial differential equations with fractional Brownian motion

Mahdieh Arezoomandan and Ali R. Soheili
Journal of Computational and Applied Mathematics 389 113369 (2021)
DOI: 10.1016/j.cam.2020.113369

## Convergence rates for the numerical approximation of the 2D stochastic Navier–Stokes equations

Dominic Breit and Alan Dodgson
Numerische Mathematik 147 (3) 553 (2021)
DOI: 10.1007/s00211-021-01181-z

## Convergence of the spectral Galerkin method for the stochastic reaction–diffusion–advection equation

Li Yang and Yanzhi Zhang
Journal of Mathematical Analysis and Applications 446 (2) 1230 (2017)
DOI: 10.1016/j.jmaa.2016.09.028

## Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs

Charles-Edouard Bréhier
Journal of Complexity 56 101424 (2020)
DOI: 10.1016/j.jco.2019.101424

## Lie–Trotter Splitting for the Nonlinear Stochastic Manakov System

André Berg, David Cohen and Guillaume Dujardin
Journal of Scientific Computing 88 (1) (2021)
DOI: 10.1007/s10915-021-01514-y