Related papers: Multi-step Richardson-Romberg Extrapolation: Remar…
This paper is concerned with the error estimation of the fast multipole method (FMM) for scattering problems in 2-D. The FMM error is caused by truncating Graf's addition theorem in each step of the algorithm, including two expansions and…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
Recently, rectified flow (RF)-based models have achieved state-of-the-art performance in many areas for both the multi-step and one-step generation. However, only a few theoretical works analyze the discretization complexity of RF-based…
This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the computational costs to different activity levels of the system.…
This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
We propose a new method of the construction of the asymptotically efficient estimator-processes asymptotically equivalent to the MLE and the same time much more easy to calculate. We suppose that the observed process is ergodic diffusion…
We propose a modification of the standard linear implicit Euler integrator for the weak approximation of parabolic semilinear stochastic PDEs driven by additive space-time white noise. The new method can easily be combined with a finite…
The continuous extension of a discrete random variable is amongst the computational methods used for estimation of multivariate normal copula-based models with discrete margins. Its advantage is that the likelihood can be derived…
Simulation of geothermal systems is challenging due to coupled physical processes in highly heterogeneous media. Combining the exponential Rosenbrock--Euler and Rosenbrock-type methods with control-volume (two-point flux approximation)…
The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…
The aim of this paper is to study the weak convergence analysis of sequence of iterates generated by a three-operator splitting method of Davis and Yin incorporated with two-step inertial extrapolation for solving monotone inclusion problem…
Error estimates for the numerical solution of the master equation are presented. Estimates are based on adjoint methods. We find that a good estimate can often be computed without spending computational effort on a dual problem. Estimates…
We aim at analyzing in terms of a.s. convergence and weak rate the performances of the Multilevel Monte Carlo estimator (MLMC) introduced in [Gil08] and of its weighted version, the Multilevel Richardson Romberg estimator (ML2R), introduced…
This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…
A practical and efficient scheme for the higher order integration of the Landau-Lifschitz-Gilbert (LLG) equation is presented. The method is based on extrapolation of the two-step explicit midpoint rule and incorporates adaptive time step…
We present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to…
We introduce an inferential framework for a wide class of semi-linear stochastic differential equations (SDEs). Recent work has shown that numerical splitting schemes can preserve critical properties of such types of SDEs, give rise to…