New regularity of Kolmogorov equation and application on approximation of semi-linear SPDEs with Hölder continuous drifts

DOI10.3934/cpaa.2019018zbMath1401.60120OpenAlexW2885665240MaRDI QIDQ1615706

Xing Huang, Chenggui Yuan, Jianhai Bao

Publication date: 31 October 2018

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2019018

zbMATH Keywords

Hölder continuitySobolev normmild solutionstochastic reaction-diffusionexponential integrator schemeZvonkin's transform

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items

Central limit theorem and self-normalized Cramér-type moderate deviation for Euler-Maruyama scheme

Cites Work

• Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift
• The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds
• Stochastic homeomorphism flows of SDEs with singular drifts and Sobolev diffusion coefficients
• Mild solutions of neutral stochastic partial functional differential equations
• A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients
• Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift
• Strong uniqueness for stochastic evolution equations with unbounded measurable drift term
• On the splitting-up method and stochastic partial differential equations
• Strong solutions of stochastic equations with singular time dependent drift
• Approximation for semilinear stochastic evolution equations
• Multilevel Monte Carlo method for parabolic stochastic partial differential equations
• \(L^p\) and almost sure convergence of a Milstein scheme for stochastic partial differential equations
• Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Hölder continuous drift coefficient
• Strong solutions of SDEs with singular drift and Sobolev diffusion coefficients
• Convergence of tamed Euler schemes for a class of stochastic evolution equations
• Degenerate SDEs in Hilbert spaces with rough drifts
• Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients
• Degenerate SDE with Hölder--Dini Drift and Non-Lipschitz Noise Coefficient
• Pathwise uniqueness and continuous dependence for SDEs with non-regular drift
• Weak approximation of stochastic partial differential equations: the nonlinear case
• On Stochastic Differential Equations with Locally Unbounded Drift
• Almost sure convergence of a semidiscrete Milstein scheme for SPDEs of Zakai type
• Numerical methods for stochastic parabolic PDEs
• The Euler-Maruyama method for S(F)DEs with Hölder drift and α-stable noise
• A numerical scheme for stochastic PDEs with Gevrey regularity
• OUP accepted manuscript
• Postprocessing for Stochastic Parabolic Partial Differential Equations
• Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise
• Stochastic Equations in Infinite Dimensions
• A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT