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First-passage time asymptotics over moving boundaries for random walk bridges. (English) Zbl 1401.60082
Summary: We study the asymptotic tail behavior of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent $$-\frac 12$$, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the return point of the random walk bridge, leading to a possible phase transition depending on the order of the distance between zero and the moving boundary.
##### MSC:
 60G50 Sums of independent random variables; random walks 60F05 Central limit and other weak theorems
##### Keywords:
random walk; first-passage time; moving boundary; bridge
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