Related papers: An Euler-Poisson Scheme for L\'evy driven SDEs
In this paper, we study the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by a additive fractional Brownian motion (fBm) with Hurst parameter $H>\frac 12$ and Poisson…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
In this paper, we study the asymptotic behavior for multi-scale stochastic differential equations driven by L\'evy processes. The optimal strong convergence order 1/2 is obtained by studying the regularity estimates for the solution of…
Two discretizations of a class of locally Lipschitz Markovian backward stochastic differential equations (BSDEs) are studied. The first is the classical Euler scheme which approximates a projection of the processes Z, and the second a novel…
In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by L\'evy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and 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 provide a abstract framework to prove total variation convergence result with arbitrary rate for numerical scheme for SDE. In particular we show that under standard weak approximation properties of scheme such as Euler we can obtain…
We consider stochastic differential equations driven by a general L\'evy processes (SDEs) with infinite activity and the related, via the Feynman-Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). We…
We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on It\^o-Taylor expansion and…
The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equations (SPDEs) defined on the whole space. Sufficient conditions…
We consider the simulation of a system of decoupled forward-backward stochastic differential equations (FBSDEs) driven by a pure jump L\'evy process $L$ and an independent Brownian motion $B$. We allow the L\'evy process $L$ to have an…
We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by L\'evy alpha-stable…
We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…
In this paper we investigate explicit numerical approximations for stochastic differential delay equations (SDDEs) under a local Lipschitz condition by employing the adaptive Euler-Maruyama (EM) method. Working in both finite and infinite…
We address the weak numerical solution of stochastic differential equations driven by independent Brownian motions (SDEs for short). This paper develops a new methodology to design adaptive strategies for determining automatically the…
We establish the first existence and uniqueness result for mild solutions of abstract stochastic evolution equations driven by arbitrary cylindrical L\'evy processes in Hilbert spaces. The coefficients are assumed to satisfy global…
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…
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type…
We consider the numerical approximation of a general second order semi--linear parabolic stochastic partial differential equation (SPDE) driven by additive space-time noise. We introduce a new modified scheme using a linear functional of…