Geodesic
Distribution of the time of attaining the maximum for the difference of the two Poisson's processes with negative linear drift
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1229-1248.

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We are considering the combination of two Poisson processes with linear drift on the whole real line in the case when negative middle drift is fulfilled. We find the distribution function for the moment of attaining the maximum for this process. As well known from monograph of Ibragimov and Khasminskii this distribution function is the limit for the distributions of normalized maximum likelihood estimators for the only discontinuous point of a density.
Keywords: Poisson process with linear drift, stochastic process with negative middle drift, probability functions of the functionals of the stochastic processes. 
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     title = {Distribution of the time of attaining the maximum for the difference of the two {Poisson's} processes with negative linear drift},
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V. E. Mosyagin; N. A. Shvemler. Distribution of the time of attaining the maximum for the difference of the two Poisson's processes with negative linear drift. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1229-1248. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a48/

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