Related papers: Asymptotic error distribution for the Euler scheme…

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…

In the present article we study strong approximation of solutions of scalar stochastic differential equations (SDEs) with bounded and $\alpha$-H\"older continuous drift coefficient and constant diffusion coefficient at time point $1$.…

We deal with approximation of solutions of delay differential equations (DDEs) via the classical Euler algorithm. We investigate the pointwise error of the Euler scheme under nonstandard assumptions imposed on the right-hand side function…

The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…

In recent years, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that may have discontinuities in space has begun. In many of these results it is assumed that the drift…

In the recent article [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there exist stochastic differential equations (SDEs) with…

We extend the taming techniques for explicit Euler approximations of stochastic differential equations (SDEs) driven by L\'evy noise with super-linearly growing drift coefficients. Strong convergence results are presented for the case of…

Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that are strongly asymptotically optimal in specific classes of…

We establish two-sided weighted integrability estimates, often referred to as a norm equivalence result, for stochastic differential equations (SDEs) with locally Lipschitz coefficients. As a key ingredient in our approach, we also derive…

Strong convergence results on tamed Euler schemes, which approximate stochastic differential equations with superlinearly growing drift coefficients that are locally one-sided Lipschitz continuous, are presented in this article. The…

On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other…

Numerical methods for stochastic differential equations with non-globally Lipschitz coefficients are currently studied intensively. This article gives an overview of our work for the case that the drift coefficient is potentially…

This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients.Under certain non-globally Lipschitz conditions, a long-time version of fundamental strong convergence theorem is established for…

We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carath\'eodory-type drift coefficients. Moreover, we also assume that both drift $f=f(t,x,z)$ and diffusion…

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

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…

Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipschitz continuous in the strong L^p-sense with respect to the…

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler…

This work focuses on the numerical approximations of random periodic solutions of stochastic differential equations (SDEs). Under non-globally Lipschitz conditions, we prove the existence and uniqueness of random periodic solutions for the…

This paper establishes the asymptotic error distribution of the tamed Euler method for stochastic differential equations (SDEs) with a coupled monotonicity condition, that is, the limit distribution of the corresponding normalized error…