相关论文: A generalized coupling approach for the weak appro…
A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…
This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…
Consider the following stochastic differential equation driven by multiplicative noise on $\mathbb{R}^d$ with a superlinearly growing drift coefficient, \begin{align*} \mathrm{d} X_t = b (X_t) \, \mathrm{d} t + \sigma (X_t) \, \mathrm{d}…
We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener…
We consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the commonly occurring small noise regime. We consider (i) standard Monte Carlo methods combined…
In this paper, we develop a general methodology to prove weak uniqueness for stochastic differential equations with coefficients depending on some path-functionals of the process. As an extension of the technique developed by Bass \&…
A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider…
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed…
Under a local one-sided Lipschitz condition, Krylov [KR] proved the existence and uniqueness of the strong solutions for stochastic differential equations by using the Euler-Maruyama approximation, where he showed that the sequence of…
We study a delayed stochastic interest rate model with superlinearly growing coefficients and develop novel analytical tools to investigate the properties of both the true solution and its truncated Euler-Maruyama (TEM) approximation. In…
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…
The numerical solutions of stochastic differential delay equations (SDDEs) under the generalized Khasminskii-type condition were discussed by Mao [15], and the theory there showed that the Euler-Maruyama (EM) numerical solutions converge to…
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…
In this work, the authors introduce a generalized weak Galerkin (gWG) finite element method for the time-dependent Oseen equation. The generalized weak Galerkin method is based on a new framework for approximating the gradient operator.…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…
This paper mainly investigates the strong convergence and stability of the truncated Euler-Maruyama (EM) method for stochastic differential delay equations with variable delay whose coefficients can be growing super-linearly. By…
This paper focuses on studying the convergence rate of the density function of the Euler--Maruyama (EM) method, when applied to the overdamped generalized Langevin equation with fractional noise which serves as an important model in many…
We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…
Euler-Maruyama method is studied to approximate stochastic differential equations driven by the symmetric $\alpha$-stable additive noise with the $\beta$ H\"older continuous drift coefficient. When $\alpha \in (1,2)$ and $\beta \in…