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.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points

2000 Mathematics Subject Classification: 60J60, 62M99.

Limit Theorems for Branching Processes with Random Migration Components

The classical Bienaymé-Galton-Watson (BGW) branching process can be interpreted as mathematical model of population dynamics when the members of an isolated population reproduce themselves independently of each other according to a stochastic law.

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights

2000 Mathematics Subject Classification: Primary 60F17, 60G52, 60G70 secondary 60E07, 62E20.

Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05

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

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.