On error rates in normal approximations and simulation schemes for Levy processes

Research output: Contribution to journalArticle

Abstract

Let X = (X(t) : t greater than or equal to 0) be a Levy 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 Levy 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, including their variability by approximating by a Brownian motion, gives successively better results in general. Finally, some numerical illustrations involving a normal inverse Gaussian Levy process are given.

Details

Authors
  • Mikael Signahl
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics

Keywords

  • divisible distributions, infinitely, normal approximation, edgeworth expansion, weak error rates
Original languageEnglish
Pages (from-to)287-298
JournalStochastic Models
Volume19
Issue number3
Publication statusPublished - 2003
Publication categoryResearch
Peer-reviewedYes