相关论文: Convergence rates of the Semi-Discrete method for …
We study the asymptotic stability of the semi-discrete (SD) numerical method for the approximation of stochastic differential equations. Recently, we examined the order of $\mathcal L^2$-convergence of the truncated SD method and showed…
We use the semi-discrete method, originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6), to reproduce qualitative…
We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…
We are interested in the numerical approximation of non-linear stochastic differential equations (SDEs) with solution in a certain domain. Our goal is to construct explicit numerical schemes that preserve that structure. We generalize the…
In this paper we are interested in the numerical solution of stochastic differential equations with non negative solutions. Our goal is to construct explicit numerical schemes that preserve positivity, even for super linear stochastic…
We study the numerical approximation of numerous processes, solutions of nonlinear stochastic differential equations, that appear in various applications such as financial mathematics and population dynamics. Between the investigated models…
In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are…
This paper studies the convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation. The filtration is general, and the spatial semi-discretization uses the standard continuous piecewise linear…
We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main…
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…
We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…
This work investigates numerical approximations of index 1 stochastic differential algebraic equations (SDAEs) with non-constant singular matrices under non-global Lipschitz conditions. Analyzing the strong convergence rates of numerical…
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…
A new explicit stochastic scheme of order 1 is proposed for solving commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The proposed method is a semi-tamed version of Milstein scheme to…
In this paper, we investigate the convergence in probability of a stochastic symplectic scheme for stochastic nonlinear Schr\"{o}dinger equation with quadratic potential and an additive noise. Theoretical analysis shows that our symplectic…
In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…
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 article is devoted to the analysis of the convergence rates of several nu- merical approximation schemes for linear and nonlinear Schr\"odinger equations on the real line. Recently, the authors have introduced viscous and two-grid…
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong…