Related papers: Logarithmic Euler Maruyama Scheme for Multi Dimens…
We study the strong $L^p$-convergence rates of the Euler-Maruyama method for stochastic differential equations driven by Brownian motion with low-regularity drift coefficients. Specifically, the drift is assumed to be in the…
The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by c\`adl\`ag paths satisfying a suitable criterion, namely the…
Recently a lot of effort has been invested to analyze the $L_p$-error of the Euler-Maruyama scheme in the case of stochastic differential equations (SDEs) with a drift coefficient that may have discontinuities in space. For scalar SDEs with…
We study in this article the strong rate of convergence of the Euler-Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik. We obtain the strong rate of convergence under similar assumptions for strong…
This work deals with the Euler-Maruyama (EM) scheme for stochastic differential equations with Markovian switching (SDEwMSs). We focus on the Lp-convergence rate (p is greater than or equal to 2) of the EM method given in this paper. As far…
In this paper, the truncated Euler-Maruyama (EM) method is employed together with the Multi-level Monte Carlo (MLMC) method to approximate the expectations of functions of solutions to stochastic differential equations (SDEs). The…
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 this paper, we show the convergence rate of Euler-Maruyama scheme for non-degenerate SDEs with Dini continuous coefficients, by the aid of the regularity of the solution to the associated Kolmogorov equation. We obtain the same…
In this paper, we study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are…
This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the…
This paper is concerned with strong convergence of the truncated Euler-Maruyama scheme for neutral stochastic differential delay equations driven by Brownian motion and pure jumps respectively. Under local Lipschitz condition, convergence…
This paper investigates the approximation of stochastic delay differential equations (SDDEs) via the backward Euler-Maruyama (BEM) method under generalized monotonicity and Khasminskii-type conditions in the infinite horizon. First, by…
This paper develops methods for numerically solving stochastic delay-differential equations (SDDEs) with multiple fixed delays that do not align with a uniform time mesh. We focus on numerical schemes of strong convergence orders $1/2$ and…
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…
The strong convergence of the semi-implicit Euler-Maruyama (EM) method for stochastic differential equations with non-linear coefficients driven by a class of L\'evy processes is investigated. The dependence of the convergence order of the…
In this paper, we introduce a linear stochastic volatility model driven by $\alpha$-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its…
In this paper, we investigate the stability equivalence problem for stochastic differential delay equations, the auxiliary stochastic differential equations and their corresponding Euler-Maruyama (EM) methods under $G$-framework. More…
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…
The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the H\"older continuity in the temporal variable and the super-linear growth in the state variable.…
Mean square exponential stability of $\theta$-EM and modified truncated Euler-Maruyama (MTEM) methods for stochastic differential delay equations (SDDEs) are investigated in this paper. We present new criterion of mean square exponential…