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.

A Cauchy Integral Related to a Robot-safety Device System

We introduce a robot-safety device system attended by two different repairmen. The twin system is characterized by the natural feature of cold standby and by an admissible “risky” state. In order to analyse the random behaviour of the entire system (robot, safety device, repair facility) we employ a stochastic process endowed with probability measures satisfying general Hokstad-type differential equations. The solution procedure is based on the theory of sectionally holomorphic functions, characterized by a Cauchy-type integral defined as a Cauchy principal value in double sense. An application of the Sokhotski-Plemelj formulae determines the long-run availability of the robot-safety device. Finally, we consider the particular but important case of deterministic repair.

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.