Related papers: High order weak approximation of Stochastic Differ…
Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for numerical…
We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence,…
We use the linear scalar SDE as a test problem to show that it is possible to construct almost sure stable first-order weak balanced schemes based on the addition of stabilizing functions to the drift terms. Then, we design balanced schemes…
The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
In recent work of Hairer, Hutzenthaler and Jentzen, see [9], a stochastic differential equation (SDE) with infinitely often differentiable and bounded coefficients was constructed such that the Monte Carlo Euler method for approximation of…
We provide a abstract framework to prove total variation convergence result with arbitrary rate for numerical scheme for SDE. In particular we show that under standard weak approximation properties of scheme such as Euler we can obtain…
Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to develop the explicit numerical method for approximating super-linear stochastic functional differential equations (SFDEs). Precisely, borrowing…
We study the weak convergence of a generic tamed Euler-Maruyama scheme for kinetic stochastic differential equations (SDEs) with integrable drifts. We show that the marginal density of the considered scheme converges at rate 1/2 to the…
We propose new jump-adapted weak approximation schemes for stochastic differential equations driven by pure-jump L\'evy processes. The idea is to replace the driving L\'evy process $Z$ with a finite intensity process which has the same…
In this paper, we are interested in the time discrete approximation of Ef(X(T)) when X is the solution of a stochastic differential equation with a diffusion coefficient function of the form |x|^a. We propose a symmetrized version of the…
This article proposes and analyzes explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (SPDEs) with polynomial nonlinearities such as, e.g.,…
We study the strong approximation of the solutions to singular stochastic kinetic equations (also referred to as second-order SDEs) driven by $\alpha$-stable processes, using an Euler-type scheme inspired by [11]. For these equations, the…
We construct a nonstandard finite difference numerical scheme to approximate stochastic differential equations (SDEs) using the idea of weighed step introduced by R.E. Mickens. We prove the strong convergence of our scheme under locally…
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 paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and…
We are investigating the first strong convergence analysis of a numerical method for stochastic differential algebraic equations (SDAEs) under a non-global Lipschitz setting. It is well known that the explicit Euler scheme fails to converge…
Weak approximations have been developed to calculate the expectation value of functionals of stochastic differential equations, and various numerical discretization schemes (Euler, Milshtein) have been studied by many authors. We present a…
We study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) which include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation. We propose a fully…
This paper aims at developing a systematic study for the weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to…