On the Wald's Sequential Probability Ratio Test for Lévy Processes

Bruno Buonaguidi, Pietro Muliere

Risultato della ricerca: Contributo in rivistaArticolo in rivista

3 Citazioni (Scopus)

Abstract

The Wald's sequential probability ratio test (SPRT) of two simple hypotheses regarding the Lévy-Khintchine triplet of a wide family of Lévy processes is analyzed: we concentrate on continuous paths and pure increasing jump Lévy processes. Appealing to the theory of Markov processes, we employ a general method for determining the stopping boundaries and the expected length of the SPRT for a given admissible pair (α, β) of error probabilities. The well-known results of the Wiener and Poisson sequential testing can be derived accordingly. The explicit solution for the SPRT of two simple hypotheses about the parameter p ∈ (0, 1) of a Lévy negative binomial process is shown. © 2013 Copyright Taylor and Francis Group, LLC.
Lingua originaleEnglish
pagine (da-a)267-287
Numero di pagine21
RivistaSequential Analysis
Volume32
DOI
Stato di pubblicazionePubblicato - 2013

Keywords

  • Fixed error probability formulation
  • Lévy processes
  • Lévy-Khintchine triplet
  • Modeling and Simulation
  • Negative binomial process
  • Optimal stopping
  • SPRT
  • Sequential testing
  • Statistics and Probability
  • Variational formulation

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