Let Xt, t ≥ 0 be a real valued process with stationary independent increments having only negative jumps. We obtain b(t) such that lim sup Xt/b(t) equals a finite positive constant with probability one as t → 0 and t → ∞ under extra condition. The hypotheses about the behavior of Lévy measure near zero and infinity are necessary to guarantee that the lim sup is positive.
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability