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

Pancheva, E.; Mitov, I.; Volkovich, Z.

Serdica Mathematical Journal (2009)

- Volume: 35, Issue: 2, page 169-194
- ISSN: 1310-6600

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topPancheva, 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 -

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