Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

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.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

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