For a class of superlinear SPDEs driven by multiplicative noise, we prove an (essentially) sharp uniform-in-time (UIT) weak convergence rate for the nonlinearity-explicit Galerkin tamed Euler method (GTEM). Under standard monotonicity assumptions, the proof combines Malliavin calculus with regularity theory for the associated backward Kolmogorov equation (BKE), leading to UIT moment, H\"older, and Malliavin estimates, along with regularity estimates for the BKE solution. These estimates, together with a weak error decomposition and Malliavin integration by parts (IBP) formula, then yield a UIT weak convergence rate $\tau^\rho+\lambda_N^{-(\rho+\gamma/2)}$ for any $\rho \in (0,1)$, where $\gamma\in[0,1)$ quantifies the assumed spatial Sobolev regularity. Consequently, we obtain a sharp ergodic error estimate between the exact and numerical invariant measures. Numerical experiments support the theory.
This paper investigates the uniform-in-time strong convergence rates of a fully discrete approximation for the stochastic Cahn--Hilliard equation driven by multiplicative noise in spatial dimensions $d\in\{1,2,3\}$. The proposed scheme combines a spectral Galerkin method in space with a backward Euler scheme in time. T...
Jia-Qi He, Nan Deng, Shuhan Zhang et al.· 1 citation
This article establishes sharp strong error estimates for the fully discrete approximation of semilinear parabolic stochastic partial differential equations (SPDEs) driven by multiplicative noise and subject to nonsmooth initial data. The spatial discretization is based on a standard finite element method, coupled with...
We investigate the dynamical behavior of a class of semilinear stochastic wave equations on a bounded smooth domain $\Ocal\subset\R^d$ driven by additive trace-class noise, where the elastic response is governed by a \emph{mixed local--nonlocal} operator $\Acal=-\theta\Delta+\beta(-\Delta)^s$ with $s\in(0,1)$. A fundam...
Francisco Delgado-Vences, Jose Julian Pavon-Español· 0 citations
In this paper, we prove pathwise uniform convergence at rates up to $1/2$ for tamed exponential Euler schemes for semilinear hyperbolic stochastic evolution equations with superlinearly growing nonlinearities and multiplicative noise. We take the term hyperbolic to mean that the leading operator generates a contractive...
We establish interior maximal $L^{q_c}$-regularity for bounded strong solutions of $u_t-\Delta u+|Du|^\gamma=f$ in $\mathbb{T}^d\times(0,T)$, where $d\geq 2$, $\gamma>2$, and $q_c=(d+2)(\gamma-1)/\gamma$. The estimates are uniform for uniformly bounded families of solutions whose source terms range over a bounded, unif...
We establish scale-invariant interior $C^{1,\alpha}$ estimates for bounded viscosity solutions of $(-\Delta)^su+b\cdot\nabla u=f$ for $s\in[1/2,1)$ with locally H\"older $b$ and $f$. The critical case uses Silvestre's parabolic theorem; the subcritical case uses Schauder estimates and interpolation. Applying this visco...
Qi Xue, Chao Zhang· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
