We consider the Euler approximation of stochastic differential equations (SDEs) driven by Levy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y = Z(V) with V a subordinator and Z a stable process, we propose an approximation Y by Z(V-n) where V-n is an approximation of V. We then compute the rate of convergence for the approximation of the solution X of an SDE driven by Y using results about the stability of SDEs. (C) 2003 Elsevier B.V. All rights reserved.
Subject classification (UKÄ)
- Probability Theory and Statistics
- stochastic differential equation
- numerical approximation
- Levy process
- shot noise representation