Related papers: A strongly convergent numerical scheme from Ensemb…
To construct positivity-preserving numerical methods, a vast majority of existing works employ transformation techniques such as the Lamperti transformation or logarithmic transformation. However, using these techniques often leads to the…
Accurate state estimates are required for increasingly complex systems, to enable, for example, feedback control. However, available state estimation schemes are not necessarily real-time feasible for certain large-scale systems. Therefore,…
This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations…
The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with…
The Euler scheme is one of the standard schemes to obtain numerical approximations of stochastic differential equations (SDEs). Its convergence properties are well-known in the case of globally Lipschitz continuous coefficients. However, in…
This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H\"older continuous drifts and locally H\"older continuous diffusion coefficients. To handle with the superlinear terms in…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler…
In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn--Hilliard equation with additive noise. The fully discrete approximation combines a spectral Galerkin method in space…
Ensemble Kalman Sampler (EKS) is a method to find approximately $i.i.d.$ samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. The continuous version of the algorithm is a set of…
In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piece-wise continuous, and whose diffusion coefficient is superlinearly growing and locally H\"older continuous. We first…
We propose a fully practical numerical scheme for the simulation of the stochastic total variation flow (STFV). The approximation is based on a stable time-implicit finite element space-time approximation of a regularized STVF equation. The…
Previously, the authors derived an analog of the Euler-Maru\-yama method (fEMM) for free stochastic differential equations (fSDEs) and proved strong convergence of order $\gamma=0.5$ in $L_1(\varphi)$-norm under certain assumptions. In this…
This work proposes ensemble Kalman randomized maximum likelihood estimation, a new derivative-free method for performing randomized maximum likelihood estimation, which is a method that can be used to generate approximate samples from…
We investigate the numerical approximation of the stochastic Allen--Cahn equation with multiplicative noise on a periodic domain. The considered scheme uses a recently proposed augmented variant of scalar auxiliary variable method for the…
We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed…
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…