Relationship between Extremal and Sum Processes Generated by the same Point Process

Pancheva, E., Mitov, I., and Volkovich, Z.. "Relationship between Extremal and Sum Processes Generated by the same Point Process." Serdica Mathematical Journal 35.2 (2009): 169-194. <http://eudml.org/doc/281365>.

@article{Pancheva2009,
abstract = {2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d as well as for the associated with it sum and extremal processes on an open subset S . The complement of S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and study sum processes over explosion area. Finally we generalize the model of u.n.t.a. to random sample size processes.},
author = {Pancheva, E., Mitov, I., Volkovich, Z.},
journal = {Serdica Mathematical Journal},
keywords = {Extremal Processes; Increasing Processes with Independent Increments; Weak Limit Theorems; Levy Measure; Poisson Point Processes; Bernoulli Point Processes; Random Sample Size; extremal processes; increasing processes with independent increments; weak limit theorems; Levy measure; Poisson point processes; Bernoulli point processes; random sample size},
language = {eng},
number = {2},
pages = {169-194},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Relationship between Extremal and Sum Processes Generated by the same Point Process},
url = {http://eudml.org/doc/281365},
volume = {35},
year = {2009},
}

TY - JOUR
AU - Pancheva, E.
AU - Mitov, I.
AU - Volkovich, Z.
TI - Relationship between Extremal and Sum Processes Generated by the same Point Process
JO - Serdica Mathematical Journal
PY - 2009
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 2
SP - 169
EP - 194
AB - 2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d as well as for the associated with it sum and extremal processes on an open subset S . The complement of S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and study sum processes over explosion area. Finally we generalize the model of u.n.t.a. to random sample size processes.
LA - eng
KW - Extremal Processes; Increasing Processes with Independent Increments; Weak Limit Theorems; Levy Measure; Poisson Point Processes; Bernoulli Point Processes; Random Sample Size; extremal processes; increasing processes with independent increments; weak limit theorems; Levy measure; Poisson point processes; Bernoulli point processes; random sample size
UR - http://eudml.org/doc/281365
ER -