相关论文: Existence, uniqueness, and approximation of soluti…

In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a…

We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient.…

We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…

In this paper we introduce a transformation technique, which can on the one hand be used to prove existence and uniqueness for a class of SDEs with discontinuous drift coefficient. One the other hand we present a numerical method based on…

In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as…

The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…

In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piece-wise continuous, and whose diffusion coefficient is superlinearly growing and locally H\"older continuous. We first…

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the…

In this paper, we study weak well-posedness of a McKean-Vlasov stochastic differential equations (SDEs) whose drift is density-dependent and whose diffusion is constant. The existence part is due to H\"older stability estimates of the…

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.

In this letter we prove existence and uniqueness of strong solutions to multi-dimensional SDEs with discontinuous drift and finite activity jumps.

Stochastic differential equations (SDEs) using jump-diffusion processes describe many natural phenomena at the microscopic level. Since they are commonly used to model economic and financial evolutions, the calibration and optimal control…

In this paper we study strong approximation of the solution of a scalar stochastic differential equation (SDE) at the final time in the case when the drift coefficient may have discontinuities in space. Recently it has been shown in…

The Euler scheme is one of the standard schemes to obtain numerical approximations of stochastic differential equations (SDEs). Its convergence properties are well-known in the case of globally Lipschitz continuous coefficients. However, in…

A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…

We study strong approximation of $d$-dimensional stochastic differential equations (SDEs) with a discontinuous drift coefficient. More precisely, we essentially assume that the drift coefficient is piecewise Lipschitz continuous with an…

In this paper, we consider scalar stochastic differential equations (SDEs) with a superlinearly growing and piecewise continuous drift coefficient. Existence and uniqueness of strong solutions of such SDEs are obtained. Furthermore, the…

Existence, uniqueness, and $L_p$-approximation results are presented for scalar stochastic differential equations (SDEs) by considering the case where, the drift coefficient has finitely many spatial discontinuities while both coefficients…

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,…

In this paper, we first establish well-posedness results for one-dimensional McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial…