AN EXACT ASYMPTOTICS FOR THE MOMENT OF CROSSING A CURVED BOUNDARY BY AN ASYMPTOTICALLY STABLE RANDOM WALK

作者：Wachtel V I^*; Denisov D E

来源：Theory of Probability and Its Applications, 2016, 60(3): 481-500.

DOI：10.1137/S0040585X97T987740

• first passage time
• moving boundary
• nonlinear boundary
• exit time

Suppose that {S-n, n >= 0} is an asymptotically stable random walk. Let g be a positive function and T-g be the first time when Sn leaves [-g(n), infinity). In this paper we study asymptotic behavior of T-g. We provide integral tests for function g that guarantee P(T-g > n) similar to V (g) P( T-0 > n), where T-0 is the first strict descending ladder epoch of {S-n}.

• 出版日期2016