Hyper-random Phenomena: Definition and Description

The paper is dedicated to the theory which describes physical phenomena in non-constant statistical conditions. The theory is a new direction in probability theory and mathematical statistics that gives new possibilities for presentation of physical world by hyper-random models. These models take into consideration the changing of object’s properties, as well as uncertainty of statistical conditions.

A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.

Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Minimization of Reactive Probabilistic Automata

The problem of finite automata minimization is important for software and hardware designing. Different types of automata are used for modeling systems or machines with finite number of states. The limitation of number of states gives savings in resources and time. In this article we show specific type of probabilistic automata: the reactive probabilistic finite automata with accepting states (in brief the reactive probabilistic automata), and definitions of languages accepted by it. We present definition of bisimulation relation for automata's states and define relation of indistinguishableness of automata states, on base of which we could effectuate automata minimization. Next we present detailed algorithm reactive probabilistic automata’s minimization with determination of its complexity and analyse example solved with help of this algorithm.

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

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.

Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80.

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

2000 Mathematics Subject Classification: 60J60, 62M99.

Well-Posedness, Conditioning and Regularization of Minimization, Inclusion and Fixed-Point Problems

AMS subject classification: 65K10, 49M07, 90C25, 90C48.

Efficient Control in Multistage Stochastic Optimization Problem

AMS subject classification: 90C31, 90A09, 49K15, 49L20.

Large Distinct Part Sizes in a Random Integer Partition

A partition of a positive integer n is a way of writing it as the sum of positive integers without regard to order; the summands are called parts. The number of partitions of n, usually denoted by p(n), is determined asymptotically by the famous partition formula of Hardy and Ramanujan [5]. We shall introduce the uniform probability measure P on the set of all partitions of n assuming that the probability 1/p(n) is assigned to each n-partition. The symbols E and V ar will be further used to denote the expectation and variance with respect to the measure P . Thus, each conceivable numerical characteristic of the parts in a partition can be regarded as a random variable.

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.