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

VL - 16

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 1

ER -