Related papers: A Strong Order 1/2 Method for Multidimensional SDE…
This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…
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…
An explicit first-order drift-randomized Milstein scheme for a regime switching stochastic differential equation is proposed and its bi-stability and rate of strong convergence are investigated for a non-differentiable drift coefficient.…
In this paper, we first prove that the existence of a solution of SDEs under the assumptions that the drift coefficient is of linear growth and path--dependent, and diffusion coefficient is bounded, uniformly elliptic and H\"older…
We study strong approximation of scalar additive noise driven stochastic differential equations (SDEs) at time point $1$ in the case that the drift coefficient is bounded and has Sobolev regularity $s\in(0,1)$. Recently, it has been shown…
Firstly, we investigate Euler-Maruyama approximation for solutions of stochastic differential equations (SDEs) driven by a symmetric \alpha\ stable process under Komatsu condition for coefficients. The approximation implies naturally the…
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 the numerical approximation of stochastic evolution equations with a monotone drift driven by an infinite-dimensional Wiener process. To discretize the equation, we combine a drift-implicit two-step BDF method for the temporal…
This paper focuses on the strong convergence of the truncated $\theta$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate,…
We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…
Previously, the authors derived an analog of the Euler-Maru\-yama method (fEMM) for free stochastic differential equations (fSDEs) and proved strong convergence of order $\gamma=0.5$ in $L_1(\varphi)$-norm under certain assumptions. In this…
We consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusive coefficient is uniformly elliptic, H\"older…
This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical…
In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only…
In this paper, our main aim is to investigate the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent $H\in(1/2, 1)$. After giving…
In this paper we study the rate of convergence of a symmetrized version of the Milstein scheme applied to the solution of the one dimensional SDE $$X_t = x_0 + \int_{0}^t{b(X_s)ds}+\int_{0}^t{\sigma |X_s|^\alpha dW_s}, \;x_0>0,\;\sigma>0,\;…
The existence-uniqueness and stability of strong solutions are proved for a class of degenerate stochastic differential equations, where the noise coeffcicient might be non-Lipschitz, and the drift is locally Dini continuous in the…
We close an unexpected gap in the literature of stochastic differential equations (SDEs) with drifts of super linear growth (and random coefficients), namely, we prove Malliavin and Parametric Differentiability of such SDEs. The former is…
An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A…
The aim of this paper is to obtain convergence in mean in the uniform topology of piecewise linear approximations of Stochastic Differential Equations (SDEs) with $C^1$ drift and $C^2$ diffusion coefficients with uniformly bounded…