Sequential Testing Problems for Lévy Processes

Bruno Buonaguidi, Pietro Muliere

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We present the sequential testing of two simple hypotheses for a large class of Lévy processes. As usual in this framework, the initial optimal stopping problem is reduced to a free-boundary problem, solved through the principles of the smooth and/or continuous fit. The well-known solutions of the Wiener and the Poisson sequential testing can be derived from our procedure. The exact solution for sequentially testing two simple hypotheses concerning the parameter p, 0 < p < 1, of a negative binomial process is explicitly given. © 2013 Copyright Taylor and Francis Group, LLC.
Original languageEnglish
Pages (from-to)47-70
Number of pages24
JournalSequential Analysis
Volume32
DOIs
Publication statusPublished - 2013

Keywords

  • Bayes decision rule
  • Free-boundary Stephan problem
  • Lévy processes
  • Modeling and Simulation
  • Negative binomial process
  • Optimal stopping
  • Principles of continuous and smooth fit
  • Sequential testing
  • Statistics and Probability

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