On error rates in normal approximations and simulation schemes for Lévy
processes
Mikael Signahl
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2002
ISSN 14039338

Abstract:

Let X = (X(t) : t /geq 0) be a Lévy process. In simulation,
one often wants to know at what size it is possible to truncate the small
jumps while retaining enough accuracy. A useful tool here is the Edgeworth
expansion. We provide a third order expansion together with a uniform error
bound, assuming third Lévy moment is 0. We next discuss approximating
X in the finite variation case. Truncating the small jumps, we show that,
adding their expected value, and further, include their variation, gives
successively better results in general. Finally, some numerical illustrations
involving a normal inverse Gaussian Lévy process are given.



Key words:

hidden Markov model, Markovmodulated Poisson process, traffic analysis,
Poissonification, likelihood estimation, state space representation, Riccati
equation, subspace identification
