TY - JOUR
T1 - On the sequence of partial maxima of some random sequences
AU - Ortega, Joaquín
AU - Wschebor, Mario
N1 - Generated from Scopus record by KAUST IRTS on 2019-11-20
PY - 1984/1/1
Y1 - 1984/1/1
N2 - Let {Xn, n ≥ 1} be a sequence of identically distributed random variables, Zn = max {X1,..., Xn} and {un, n ≥ 1 } an increasing sequence of real numbers. Under certain additional requirements, necessary and sufficient conditions are given to have, with probability one, an infinite number of crossings of {Zn} with respect to {un}, in two cases: (1) The Xn's are independent, (2) {Xn} is stationary Gaussian and satisfies a mixing condition. © 1983.
AB - Let {Xn, n ≥ 1} be a sequence of identically distributed random variables, Zn = max {X1,..., Xn} and {un, n ≥ 1 } an increasing sequence of real numbers. Under certain additional requirements, necessary and sufficient conditions are given to have, with probability one, an infinite number of crossings of {Zn} with respect to {un}, in two cases: (1) The Xn's are independent, (2) {Xn} is stationary Gaussian and satisfies a mixing condition. © 1983.
UR - https://linkinghub.elsevier.com/retrieve/pii/0304414984901777
UR - http://www.scopus.com/inward/record.url?scp=0042322660&partnerID=8YFLogxK
U2 - 10.1016/0304-4149(84)90177-7
DO - 10.1016/0304-4149(84)90177-7
M3 - Article
SN - 0304-4149
VL - 16
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 1
ER -