相关论文: Error estimates for the robust $\alpha$-stable cen…

We consider numerical schemes for computing the linear response of steady-state averages of stochastic dynamics with respect to a perturbation of the drift part of the stochastic differential equation. The schemes are based on Girsanov's…

Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…

Optimizing over the stationary distribution of stochastic differential equations (SDEs) is computationally challenging. A new forward propagation algorithm has been recently proposed for the online optimization of SDEs. The algorithm solves…

We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…

In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator…

We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…

In this paper, the a posteriori error estimates of the exponential midpoint method for time discretization are studied for linear and semilinear parabolic equations. Using the exponential midpoint approximation defined by a continuous and…

In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…

We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…

This paper is concerned with error estimates of the fully discrete generalized finite element method (GFEM) with optimal local approximation spaces for solving elliptic problems with heterogeneous coefficients. The local approximation…

We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…

Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid in time and space with infill asymptotics in…

Convergence results for the immersed boundary method applied to a model Stokes problem with the homogeneous Dirichlet boundary condition are presented. As a discretization method, we deal with the finite element method. First, the immersed…

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…