Random sums of independent indicators and generalized reduced processes

I. Rahimov

doi:10.1081/SAP-120017539

Random sums of independent indicators and generalized reduced processes

I. Rahimov^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider a random sum of independent and identically distributed Bernoulli random variables. We prove several limit theorems for this sum under some natural assumptions. Using these limit theorems a generalized version of the reduced critical Galton-Watson process will be studied. In particular we find limit distributions for the number of individuals in a given generation the number of whose descendants after some generations exceeds a fixed or increasing level. An application to study of the number of "big" trees in a forest containing a random number of trees will also be discussed.

Original language	English
Pages (from-to)	205-221
Number of pages	17
Journal	Stochastic Analysis and Applications
Volume	21
Issue number	1
DOIs	https://doi.org/10.1081/SAP-120017539
State	Published - 2003

Bibliographical note

Funding Information:
The author acknowledges excellent research facilities in the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. This research was supported by KFUPM (Research Project #2–1/2002–2003).

Keywords

Bernoulli random variables
Large population
Normal
Random sums
Reduced process
Reduction
Tree
Vertex

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Access to Document

10.1081/SAP-120017539

Cite this

@article{5343907e3ea441ee8e88d0c52414332f,

title = "Random sums of independent indicators and generalized reduced processes",

abstract = "We consider a random sum of independent and identically distributed Bernoulli random variables. We prove several limit theorems for this sum under some natural assumptions. Using these limit theorems a generalized version of the reduced critical Galton-Watson process will be studied. In particular we find limit distributions for the number of individuals in a given generation the number of whose descendants after some generations exceeds a fixed or increasing level. An application to study of the number of {"}big{"} trees in a forest containing a random number of trees will also be discussed.",

keywords = "Bernoulli random variables, Large population, Normal, Random sums, Reduced process, Reduction, Tree, Vertex",

author = "I. Rahimov",

note = "Funding Information: The author acknowledges excellent research facilities in the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. This research was supported by KFUPM (Research Project \#2–1/2002–2003).",

year = "2003",

doi = "10.1081/SAP-120017539",

language = "English",

volume = "21",

pages = "205--221",

journal = "Stochastic Analysis and Applications",

issn = "0736-2994",

publisher = "Taylor and Francis Ltd.",

number = "1",

}

TY - JOUR

T1 - Random sums of independent indicators and generalized reduced processes

AU - Rahimov, I.

N1 - Funding Information: The author acknowledges excellent research facilities in the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. This research was supported by KFUPM (Research Project #2–1/2002–2003).

PY - 2003

Y1 - 2003

N2 - We consider a random sum of independent and identically distributed Bernoulli random variables. We prove several limit theorems for this sum under some natural assumptions. Using these limit theorems a generalized version of the reduced critical Galton-Watson process will be studied. In particular we find limit distributions for the number of individuals in a given generation the number of whose descendants after some generations exceeds a fixed or increasing level. An application to study of the number of "big" trees in a forest containing a random number of trees will also be discussed.

AB - We consider a random sum of independent and identically distributed Bernoulli random variables. We prove several limit theorems for this sum under some natural assumptions. Using these limit theorems a generalized version of the reduced critical Galton-Watson process will be studied. In particular we find limit distributions for the number of individuals in a given generation the number of whose descendants after some generations exceeds a fixed or increasing level. An application to study of the number of "big" trees in a forest containing a random number of trees will also be discussed.

KW - Bernoulli random variables

KW - Large population

KW - Normal

KW - Random sums

KW - Reduced process

KW - Reduction

KW - Tree

KW - Vertex

UR - https://www.scopus.com/pages/publications/0037285131

U2 - 10.1081/SAP-120017539

DO - 10.1081/SAP-120017539

M3 - Article

AN - SCOPUS:0037285131

SN - 0736-2994

VL - 21

SP - 205

EP - 221

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 1

ER -

Random sums of independent indicators and generalized reduced processes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this