scholarly journals Extinction Moment for a Branching Tree Evolution with Birth Rate and Death Rate Both Depending on Age

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Xi Hu ◽  
Yun-Zhi Yan ◽  
Zhong-Tuan Zheng ◽  
Hong-Yan Li ◽  
Hong-Yan Zhao
Keyword(s):  
Approximation Algorithm ◽  
Nuclear Physics ◽  
Death Rate ◽  
Birth Rate ◽  
Branching Process ◽  
Analytical Formula ◽  
Extinction Probability ◽  
Extinction Time ◽  
Necessary And Sufficient ◽  
First Time

In this paper, a branching tree evolution is established, in which the birth rate and the death rate are both dependent on node’s age. The extinction probability and the t-pre-extinction (extinct before time t ) probability are studied, by which the distribution of the extinction moment can be given. The analytical formula and the approximation algorithm for the distribution of extinction moment are given; furthermore, the analytical formula and the approximation algorithm of extinction probability are given, and a necessary and sufficient condition of extinction with probability 1 is given. It is the first time to study the distribution of extinction time for the branching process with birth rate and the death rate both depending on node’s age, and the results will do great help in the theory of branching process. It is expected to be applied in the fields of biology, genetics, medicine, epidemiology, demography, nuclear physics, actuarial mathematics, algorithm, and data structures, etc.

scholarly journals Extinction Probability of Interacting Branching Collision Processes

2012 ◽  
Vol 44 (1) ◽  
pp. 226-259 ◽  
Author(s):  
Anyue Chen ◽  
Junping Li ◽  
Yiqing Chen ◽  
Dingxuan Zhou
Keyword(s):  
Branching Process ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Extinction Probability ◽  
Hitting Times ◽  
Collision Process ◽  
Markov Branching Process ◽  
Extinction Probabilities ◽  
Collision Processes ◽  
Necessary And Sufficient

We consider the uniqueness and extinction properties of the interacting branching collision process (IBCP), which consists of two strongly interacting components: an ordinary Markov branching process and a collision branching process. We establish that there is a unique IBCP, and derive necessary and sufficient conditions for it to be nonexplosive that are easily checked. Explicit expressions are obtained for the extinction probabilities for both regular and irregular cases. The associated expected hitting times are also considered. Examples are provided to illustrate our results.

scholarly journals On the extinction times of varying and random environment branching processes

1975 ◽  
Vol 12 (01) ◽  
pp. 39-46 ◽  
Author(s):  
Alan Agresti
Keyword(s):  
Random Environment ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Extinction Time ◽  
Probability Of Extinction ◽  
Stochastically Bounded ◽  
Necessary And Sufficient ◽  
Varying Environment

Bounds are derived for the probability of extinction by the nth generation for a branching process in a varying environment. From these bounds, necessary and sufficient conditions are established for such a process to become extinct with probability one. The extinction time of a random environment branching process in which the environmental random variables are independent but not necessarily identically distributed is stochastically bounded by the extinction times of two varying environment processes.

scholarly journals On the extinction times of varying and random environment branching processes

1975 ◽  
Vol 12 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Alan Agresti
Keyword(s):  
Random Environment ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Extinction Time ◽  
Probability Of Extinction ◽  
Stochastically Bounded ◽  
Necessary And Sufficient ◽  
Varying Environment

Bounds are derived for the probability of extinction by the nth generation for a branching process in a varying environment. From these bounds, necessary and sufficient conditions are established for such a process to become extinct with probability one. The extinction time of a random environment branching process in which the environmental random variables are independent but not necessarily identically distributed is stochastically bounded by the extinction times of two varying environment processes.

Extinction Probability of Interacting Branching Collision Processes

2012 ◽  
Vol 44 (01) ◽  
pp. 226-259 ◽  
Author(s):  
Anyue Chen ◽  
Junping Li ◽  
Yiqing Chen ◽  
Dingxuan Zhou
Keyword(s):  
Branching Process ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Extinction Probability ◽  
Hitting Times ◽  
Collision Process ◽  
Markov Branching Process ◽  
Extinction Probabilities ◽  
Collision Processes ◽  
Necessary And Sufficient

We consider the uniqueness and extinction properties of the interacting branching collision process (IBCP), which consists of two strongly interacting components: an ordinary Markov branching process and a collision branching process. We establish that there is a unique IBCP, and derive necessary and sufficient conditions for it to be nonexplosive that are easily checked. Explicit expressions are obtained for the extinction probabilities for both regular and irregular cases. The associated expected hitting times are also considered. Examples are provided to illustrate our results.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Cultural Factors Affecting the Negotiation of First Sexual Intercourse among Latina Adolescent Mothers

1998 ◽  
Vol 18 (1) ◽  
pp. 121-137 ◽  
Author(s):  
Pamela I. Erickson
Keyword(s):  
Los Angeles ◽  
Sexual Intercourse ◽  
Adolescent Mothers ◽  
Social Factors ◽  
Birth Rate ◽  
Factors Affecting ◽  
First Sexual Intercourse ◽  
Latina Adolescent Mothers ◽  
Adolescent Birth ◽  
First Time

In 1995, the Latina adolescent birth rate surpassed that of African Americans for the first time. This article investigates cultural and social factors affecting the initiation of sexual intercourse among Latina adolescent mothers in Los Angeles. The data are from life history interviews with forty young mothers and their partners conducted in 1994 to 1997. Results suggest that sexual intercourse is initiated within the context of the couple's developing relationship, and that the course of relationships is highly scripted. Men pressure for sex and women resist. Women should be ignorant about sex, but control access to intercourse. Sex is never discussed. Thus, it is unexpected, and contraception other than withdrawal is not used. This script places young Latinas at enormous risk for pregnancy and STDs.

Interest rate option hedging portfolios without bank account

2019 ◽  
Vol 37 (1) ◽  
pp. 134-142
Author(s):  
Alberto Bueno-Guerrero
Keyword(s):  
Design Methodology ◽  
Contingent Claim ◽  
Necessary And Sufficient Condition ◽  
Barrier Option ◽  
Bank Account ◽  
Content Type ◽  
Option Hedging ◽  
Hedging Portfolio ◽  
Necessary And Sufficient ◽  
First Time

Purpose This paper aims to study the conditions for the hedging portfolio of any contingent claim on bonds to have no bank account part. Design/methodology/approach Hedging and Malliavin calculus techniques recently developed under a stochastic string framework are applied. Findings A necessary and sufficient condition for the hedging portfolio to have no bank account part is found. This condition is applied to a barrier option, and an example of a contingent claim whose hedging portfolio has a bank account part different from zero is provided. Originality/value To the best of the authors’ knowledge, this is the first time that this issue has been addressed in the literature.

scholarly journals Period-Life of a Branching Process with Migration and Continuous Time

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 868
Author(s):  
Khrystyna Prysyazhnyk ◽  
Iryna Bazylevych ◽  
Ludmila Mitkova ◽  
Iryna Ivanochko
Keyword(s):  
Random Process ◽  
Generating Function ◽  
Continuous Time ◽  
Branching Process ◽  
Probability Generating Function ◽  
Time Interval ◽  
The Moment ◽  
First Time ◽  
Critical Branching Process ◽  
Number Of Particles

The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life τ, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. The probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained. The boundary theorem for the period-life of the subcritical or critical branching process with migration was found.

Birth Control: Reversal or Postponement?

1960 ◽  
Vol 3 ◽  
pp. 59-73 ◽  
Author(s):  
Leo A. Orleans
Keyword(s):  
Natural Resources ◽  
Birth Control ◽  
Death Rate ◽  
Birth Rate ◽  
Natural Increase ◽  
Vital Rates ◽  
The People ◽  
The World ◽  
Communist China ◽  
Annual Population

Whereas throughout most of the world the results of the 1953 censusregistration of Communist China, reporting a population of 582·6 million, evoked anxiety and even alarm, the Communists expressed only pride and overwhelming confidence. As a people “liberated from the oppressive chains of capitalism,” Communist leaders felt that their horizons were unlimited and that feeding and caring for a population of this size presented no problems under a system in which people are “the most precious of all categories of capital.” The simultaneous release of vital rates which indicated a birth rate of 37 per thousand population and a death rate of 17 per thousand, further stressed the “great vitality of the people of new China.” The 2 per cent, natural increase (excess of births over deaths), resulting in an annual population growth of some 12 million, was declared, in line with Marxist doctrine, to be an asset in a country with vast new lands and unexploited natural resources, where additional people create additional wealth.

A note on the subcritical generalized age-dependent branching process

1976 ◽  
Vol 13 (4) ◽  
pp. 798-803 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
The Mean ◽  
Mean Function ◽  
Necessary And Sufficient

For a subcritical Bellman-Harris process for which the Malthusian parameter α exists and the mean function M(t)∼ aeat as t → ∞, a necessary and sufficient condition for e–at (1 –F(s, t)) to have a non-zero limit is known. The corresponding condition is given for the generalized branching process.

Sign in / Sign up

Export Citation Format

Share Document