Computation of the invariant measure for a Lévy driven SDE: Rate of convergence

Details Computation of the invariant measure for a Lévy driven SDE: Rate of convergence Computation of the invariant measure for a Lévy driven SDE: Rate of convergence

2006-11-03

arxiv.org/abs/math/0611072v1

Mathematics

Probability

Scientific paper

We study the rate of convergence of some recursive procedures based on some "exact" or "approximate" Euler schemes which converge to the invariant measure of an ergodic SDE driven by a L\'{e}vy process. The main interest of this work is to compare the rates induced by exact and approximate Euler schemes. In our main result, we show that replacing the small jumps by a Brownian component in the approximate case preserves the rate induced by the exact Euler scheme for a large class of L\'{e}vy processes.

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