Simulation and approximation of 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...

Simulation and Approximation of Lévy-driven Stochastic Differential Equations

We consider the problem of the simulation of Lévy-driven stochastic differential equations. It is generally impossible to simulate the increments of a Lévy-process. Thus in addition to an Euler scheme, we have to simulate approximately these increments. We use a method in which the large jumps are simulated exactly, while the small jumps are approximated by Gaussian variables. Using some recent...

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...

strong approximation for itô stochastic differential equations

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion