相关论文: A new extrapolation method for weak approximation …

In this paper, a weak Local Linearization scheme for Stochastic Differential Equations (SDEs) with multiplicative noise is introduced. First, for a time discretization, the solution of the SDE is locally approximated by the solution of the…

We present a novel extrapolation scheme for high order series expansions. The idea is to express the series, obtained in orders of an external variable, in terms of an internal parameter of the system. Here we apply this method to the…

In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function $\alpha(t)\in(0,1)$, we develop an exponential-sum-approximation (ESA) technique to approach the VO Caputo fractional derivative. The ESA…

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…

We study the emission of soft photons coupling to high energy fixed angle scattering processes at first order in the electromagnetic coupling but to all loop orders in a class of theories without soft divergences, including massive and…

In this paper, we propose a novel extrapolation coefficient scheme within a new extrapolation term and develop an accelerated proximal gradient algorithm. We establish that the algorithm achieves a sublinear convergence rate. The proposed…

We introduce a new numerical approximation method for functionals of factor credit portfolio models based on the theory of mod-$\phi$ convergence and mod-$\phi$ approximation schemes. The method can be understood as providing correction…

We present two approaches for enhancing the accuracy of second order finite difference approximations of two-dimensional semilinear parabolic systems. These are the fourth order compact difference scheme and the fourth order scheme based on…

We develop a systematic analytical approximation scheme for the singular value decompositions of arbitrary complex three dimensional matrices Y with non-degenerate singular values. We derive exact expressions for the errors of this…

The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…

We discuss a path toward the generalisation of the nested soft-collinear subtraction scheme to arbitrary $2\rightarrow n$ processes. The scheme is designed to provide an efficient and process-independent procedure to extract and regulate…

High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…

In this paper we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations. The centered polynomial is introduced for…

We study an algorithm which has been proposed by Chinesta et al. to solve high-dimensional partial differential equations. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum.…

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

A fourth-order multi-exponential scheme is proposed for the Zakharov-Shabat system. The scheme represents a product of 13 exponential operators. The construction of the scheme is based on a fourth-order three-exponential scheme, which…

Projection-based Reduced Order Models minimize the discrete residual of a "full order model" (FOM) while constraining the unknowns to a reduced dimension space. For problems with symmetric positive definite (SPD) Jacobians, this is…

We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions $F_\alpha$ for $\alpha<\omega^\omega$, hence…

We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that WVA experiment can also be implemented by a second-order correlated system. We then build two-dimensional…

We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…