相关论文: On the existence of negative moments for some non-…

In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…

We introduce a semi-implicit Euler-Maruyama approximation which preservers the non-colliding property for some class of non-colliding particle systems such as Dyson Brownian motions, Dyson-Ornstein-Uhlenbeck processes and Brownian particles…

Building on the well-posedness of the backward Kolmogorov partial differential equation in the Wasserstein space, we analyze the strong and weak convergence rates for approximating the unique solution of a class of McKean-Vlasov stochastic…

The aim of this paper is to study weak and strong convergence of the Euler--Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation $\mathrm{d} X_t=\sigma(X_t) \mathrm{d} W_t$ with non-sticky condition.…

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…

This paper studies the convergence rate of the Euler-Maruyama scheme for systems of interacting particles used to approximate solutions of nonlinear Fokker-Planck equations with singular interaction kernels, such as the Keller-Segel model.…

We introduce a semi-implicit Milstein approximation scheme for some class of non-colliding particle systems modeled by systems of stochastic differential equations with non-constant diffusion coefficients. We show that the scheme converges…

We consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a…

We study the strong existence and uniqueness of solutions within a Weyl chamber for a class of time-dependent particle systems driven by multiplicative noise. This class includes well-known processes in physics and mathematical finance. We…

In this paper, we consider the weak convergence of the Euler-Maruyama approximation for one dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local…

In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous.

We study the strong rates of the Euler-Maruyama approximation for one dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and diffusion coefficient is H\"older continuous.…

An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz…

A novel particle merging algorithm for rarefied gas dynamics simulations is proposed that can conserve arbitrary velocity and spatial moments of the particle distribution via solving a non-negative least squares problem. An extension that…

In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional stochastic differential equations with a non-linear drift, in the sense of McKean-Vlasov, driven by a…

In this paper, we investigate the weak convergence rate of Euler-Maruyama's approximation for stochastic differential equations with irregular drifts. Explicit weak convergence rates are presented if drifts satisfy an integrability…

We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…

This work establishes the weak convergence of Euler-Maruyama's approximation for stochastic differential equations (SDEs) with singular drifts under the integrability condition in lieu of the widely used growth condition. This method is…

We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to external ones, and resulting into a nonlocal version of the…

In the present work, a novel particle merging scheme is proposed for PIC-DSMC simulations, based on the solution of a Non-negative Least Squares problem. The merging algorithm conserves arbitrary moments of the velocity distribution…