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Approximating the invariant measure and the expectation of the functionals for parabolic stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients is an active research area and is far from being well understood. In this article, we study such problem in terms of a full discretization based on the spectral Galerkin method and the temporal implicit Euler scheme. By deriving the a priori estimates and regularity estimates of the numerical solution via a variational approach and Malliavin calculus, we establish the sharp weak convergence rate of the full discretization. When the SPDE admits a unique $V$-uniformly ergodic invariant measure, we prove that the invariant measure can be approximated by the full discretization. The key ingredients lie on the time-independent weak convergence analysis and time-independent regularity estimates of the corresponding Kolmogorov equation. Finally, numerical experiments confirm the theoretical findings.
In this article we formalize the problem of modeling social networks into a measure-valued process and interacting particle system. We obtain a model that describes in continuous time each vertex of the graph at a latent spatial state as a Dirac meas
In this article, we consider the stochastic Cahn--Hilliard equation driven by space-time white noise. We discretize this equation by using a spatial spectral Galerkin method and a temporal accelerated implicit Euler method. The optimal regularity pro
A novel class of implicit Milstein type methods is devised and analyzed in the present work for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffusion coefficients. By incorporating a pair of method parameters $theta
We consider a generalisation of Ulams method for approximating invariant densities of one-dimensional chaotic maps. Rather than use piecewise constant polynomials to approximate the density, we use polynomials of degree n which are defined by the req
Lipschitz bandits is a prominent version of multi-armed bandits that studies large, structured action spaces such as the [0,1] interval, where similar actions are guaranteed to have similar rewards. A central theme here is the adaptive discretization