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 originale | English |
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pagine (da-a) | 267-287 |
Numero di pagine | 21 |
Rivista | Sequential Analysis |
Volume | 32 |
DOI | |
Stato di pubblicazione | Pubblicato - 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