TY - JOUR
T1 - The Tail of the Length of an Excursion in a Trap of Random Size
AU - Gantert, Nina
AU - Klenke, Achim
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/9
Y1 - 2022/9
N2 - Consider a random walk with a drift to the right on { 0 , … , k} where k is random and geometrically distributed. We show that the tail P[T> t] of the length T of an excursion from 0 decreases up to constants like t-ϱ for some ϱ> 0 but is not regularly varying. We compute the oscillations of tϱP[T>t] as t→ ∞ explicitly.
AB - Consider a random walk with a drift to the right on { 0 , … , k} where k is random and geometrically distributed. We show that the tail P[T> t] of the length T of an excursion from 0 decreases up to constants like t-ϱ for some ϱ> 0 but is not regularly varying. We compute the oscillations of tϱP[T>t] as t→ ∞ explicitly.
KW - Excursions of random walks
KW - Tail of the population size in a branching process in random environment
KW - Tails of hitting times
KW - Trapping phenomena
UR - http://www.scopus.com/inward/record.url?scp=85133513576&partnerID=8YFLogxK
U2 - 10.1007/s10955-022-02957-9
DO - 10.1007/s10955-022-02957-9
M3 - Article
AN - SCOPUS:85133513576
SN - 0022-4715
VL - 188
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 3
M1 - 27
ER -