Linear-implicit versions of strong Taylor numerical schemes for finite dimensional It6 stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an 7 strong linear-implicit Taylor scheme with time-step A applied to the N dimensional It6-Galerkin SDE for a class of parabolic stochastic partial diff...

The Bayesian computer model calibration method has proven to be effective in a wide range of applications. In this framework, input parameters are tuned by comparing model outputs to observations. However, this methodology becomes computationally expensive for large spatial model outputs. To overcome this challenge, we employ a truncated basis representations of the model outputs. We then aim t...

This paper introduces SPDE bridges with observation noise and contains an analysis of their spatially semidiscrete approximations. The SPDEs are considered in the form mild solutions abstract Hilbert space framework suitable for parabolic equations. They assumed to be linear additive a cylindrical Wiener process. observational is also formulated via conditional distributions Gaussian random var...

Stochastically perturbed Korteweg-de Vries (KdV) equations are widely used to describe the effect of random perturbations on coherent solitary waves. We present a collective coordinate approach waves in stochastically KdV equations. The allows one reduce infinite-dimensional stochastic partial differential equation (SPDE) finite-dimensional for amplitude, width and location wave. reduction prov...

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of random tangent vector field on unit sphere. The SPDE is governed by diffusion operator Lévy-type behaviour spatial solution, derivative in time depict intermittency its temporal and driven vector-valued Brownian motion sphere characterize long-range dependence. solution presented form Kar...

An innnite system of stochastic diierential equations for the locations and weights of a collection of particles is considered. The particles interact through their weighted empirical measure, V , and V is shown to be the unique solution of a nonlinear stochastic partial diierential equation (SPDE). Conditions are given under which the weighted empirical measure has an L 2-density with respect ...

Abstract We consider a stochastic partial differential equation (SPDE) model for chemorepulsion, with non-linear sensitivity on the one-dimensional torus. By establishing an priori estimate independent of initial data, we show that there exists pathwise unique, global solution to SPDE. Furthermore, associated semi-group is Markov and possesses unique invariant measure, supported Hölder–Besov sp...

Abstract Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling numerical solutions multilevel hierarchy needed to obtain efficiency gains. In this work, we show indeed also when MLMC stochastic partial differential equations (SPDE) reac...

Abstract Bistability is a key property of many systems arising in the nonlinear sciences. For example, it appears partial differential equations (PDEs). scalar bistable reaction-diffusions PDEs, case even has taken on different names within communities such as Allee, Allen-Cahn, Chafee-Infante, Nagumo, Ginzburg-Landau, $$\Phi ^4$$ <mml:m...