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.

Buonaguidi, B., Muliere, P., On the Wald's Sequential Probability Ratio Test for Lévy Processes, <<SEQUENTIAL ANALYSIS>>, 2013; 32 (3): 267-287. [doi:10.1080/07474946.2013.803799] [http://hdl.handle.net/10807/133716]

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

Buonaguidi, Bruno
Primo
;
2013

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.
2013
Inglese
Buonaguidi, B., Muliere, P., On the Wald's Sequential Probability Ratio Test for Lévy Processes, <<SEQUENTIAL ANALYSIS>>, 2013; 32 (3): 267-287. [doi:10.1080/07474946.2013.803799] [http://hdl.handle.net/10807/133716]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/133716
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