Almost Sure Relative Stability of the Overshoot of Power Law Boundaries
نویسندگان
چکیده
We give necessary and sufficient conditions for the almost sure (a.s.) relative stability of the overshoot of a random walk when it exits from a two-sided symmetric region with curved boundaries. The boundaries are of power-law type, ±rn, r > 0, n = 1, 2, · · · , where 0 ≤ b < 1, b 6= 1/2. In these cases, the a.s. stability occurs if and only if the mean step length of the random walk is finite and nonzero, or the step length has a finite variance and mean zero. 2000 MSC Subject Classifications: primary: 60J15, 60F15, 602K05, 60G40 secondary: 60F05
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