Optimal simulation schemes for Lévy driven stochastic differential equations

Optimal simulation schemes for Lévy driven stochastic differential equations

We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Lévy process with a high order scheme for the Brownian driven component, applied between the jump times. The overall approximation is analyzed using a stochastic...

An Euler-Poisson scheme for Lévy driven stochastic differential equations

We describe an Euler scheme to approximate solutions of Lévy driven stochastic differential equations (SDEs) where the grid points are given by the arrival times of a Poisson process and thus are random. This result extends the previous work of FerreiroCastilla et al. (2014). We provide a complete numerical analysis of the algorithm to approximate the terminal value of the SDE and prove that th...

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Simulation & Stochastic Differential Equations

The Euler Scheme for Lévy Driven Stochastic Differential Equations : Limit Theorems

We study the Euler scheme for a stochastic differential equation driven by a Lévy process Y . More precisely, we look at the asymptotic behavior of the normalized error process un(X −X), where X is the true solution and X is its Euler approximation with stepsize 1/n, and un is an appropriate rate going to infinity: if the normalized error processes converge, or are at least tight, we say that t...