Some Theoretical Results on the Progeny of a Bisexual Galton-Watson Branching Process

A Superadditive Bisexual Galton-Watson Branching Process is considered and the total number of mating units, females and males, until the n-th generation, are studied. In particular some results about the stochastic monotony, probability generating functions and moments are obtained. Finally, the limit behaviour of those variables suitably normed is investigated.

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

2000 Mathematics Subject Classification: 60J80.

On the Maximum of a Branching Process Conditioned on the Total Progeny

The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.

The Maximal Number of Particles in a Branching Process with State-Dependent Immigration

AMS subject classification: 60J80, 60J15.

Option Pricing by Branching Process

2000 Mathematics Subject Classification: 60J80, 62P05.

Subcritical Randomly Indexed Branching Processes

2000 Mathematics Subject Classification: 60J80, 62P05.

Asymptotic Behaviour of a Supercritical Galton-Watson Process with Controlled Binomial Migration

AMS subject classification: 60J80, 62F12, 62P10.

Robust Estimation in Multitype Branching Processes Based on their Asymptotic Properties

2000 Mathematics Subject Classification: 60J80.

Bootstrap for Critical Branching Process with Non-Stationary Immigration

2000 Mathematics Subject Classification: Primary 60J80, Secondary 62F12, 60G99.

Some Probabilistic Results in a Bisexual Branching Process with Immigration

2000 Mathematics Subject Classification: 60J80.

Estimation of the Offspring Mean in a General Single-Type Size-Dependent Branching Process

2000 Mathematics Subject Classification: 60J80, 62F12, 62P10

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05

Crump-Mode-Jagers Branching Process: Modelling and Application for Human Population

2010 Mathematics Subject Classification: 60J85, 92D25.

Branching Stochastic Processes: History, Theory, Applications

Косто В. Митов - Разклоняващите се стохастични процеси са модели на популационната динамика на обекти, които имат случайно време на живот и произвеждат потомци в съответствие с дадени вероятностни закони. Типични примери са ядрените реакции, клетъчната пролиферация, биологичното размножаване, някои химични реакции, икономически и финансови явления. В този обзор сме се опитали да представим съвсем накратко някои от най-важните моменти и факти от историята, теорията и приложенията на разклоняващите се процеси.

A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.