Geodesic
Asymptotics for the distribution of the time of attaining the maximum for a trajectory of a Poisson process with linear drift and intensity switch
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 1, pp. 94-109
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We find the exact asymptotics of the distribution of the time when the trajectory of the process $Y(t)=at-\nu_+(pt)+\nu_-(-qt)$, $t\in(-\infty,\infty)$ attains its maximum, where $\nu_{\pm}(t)$ are independent standard Poisson processes extended by zero on the negative semiaxis. The parameters $a$, $p$, $q$ are assumed just to satisfy the condition $\mathbf{E}Y(t)<0$, $t\neq 0$.
Keywords: Poisson process with linear drift, random process with negative mean drift, exact asymptotics of distribution tails. 
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V. E. Mosyagin. Asymptotics for the distribution of the time of attaining the maximum for a trajectory of a Poisson process with linear drift and intensity switch. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 1, pp. 94-109. http://geodesic.mathdoc.fr/item/TVP_2021_66_1_a4/

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