Exact large deviation function and closed-form conditional mean first-passage time derived for Poisson process crossing linear moving barrier.
Zacks,Sample path analysis and distributions of boundary crossing times, Lecture Notes in Mathematics (Springer, Cham, 2017)
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A first passage problem for a Poisson counting process with a linear moving boundary
Exact large deviation function and closed-form conditional mean first-passage time derived for Poisson process crossing linear moving barrier.