TY - JOUR
T1 - A local limit theorem for random walk maxima with heavy tails
AU - Asmussen, Søren
AU - Kalashnikov, Vladimir
AU - Konstantinides, Dimitrios
AU - Klüppelberg, Claudia
AU - Tsitsiashvili, Gurami
PY - 2002/2/15
Y1 - 2002/2/15
N2 - For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution π of the maximum has a tail π(x, ∞) which is asymptotically proportional to ∫∞x F(y, ∞) dy. We supplement here this by a local result showing that π(x,x + z] is asymptotically proportional to zF (x, ∞).
AB - For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution π of the maximum has a tail π(x, ∞) which is asymptotically proportional to ∫∞x F(y, ∞) dy. We supplement here this by a local result showing that π(x,x + z] is asymptotically proportional to zF (x, ∞).
KW - Integrated tail
KW - Ladder height
KW - Subexponential distribution
UR - https://www.scopus.com/pages/publications/0037082552
U2 - 10.1016/S0167-7152(02)00033-0
DO - 10.1016/S0167-7152(02)00033-0
M3 - Article
AN - SCOPUS:0037082552
SN - 0167-7152
VL - 56
SP - 399
EP - 404
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 4
ER -