DSpace Collection: 2000 Volume 13
http://hdl.handle.net/10525/2113
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Limit Theorems for Branching Processes with Random Migration Components
http://hdl.handle.net/10525/2174
Title: Limit Theorems for Branching Processes with Random Migration Components<br/><br/>Authors: Yanev, George; Yanev, Nickolay<br/><br/>Abstract: 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.Evaluating the Risk in Selection Problems
http://hdl.handle.net/10525/2173
Title: Evaluating the Risk in Selection Problems<br/><br/>Authors: Stoimenova, Eugenia<br/><br/>Abstract: The procedure used should guarantee that the risk of decision asserted from the observations is at most some specified value P*.On Self-Similar Extremal Processes
http://hdl.handle.net/10525/2172
Title: On Self-Similar Extremal Processes<br/><br/>Authors: Pancheva, Elisaveta<br/><br/>Abstract: We study the limit behaviour of the sequence of extremal processes under a regularity condition on the norming sequence ζn and asymptotic negligibility of the max-increments of Yn.A System for Simulation and Estimation of Branching Processes
http://hdl.handle.net/10525/2171
Title: A System for Simulation and Estimation of Branching Processes<br/><br/>Authors: Nitcheva, Daniela; Yanev, Nickolay<br/><br/>Abstract: A computer code system for simulation and estimation of branching processes isproposed. Using the system, samples for some models with or without migration aregenerated. Over these samples we compare some properties of various estimators.Large Distinct Part Sizes in a Random Integer Partition
http://hdl.handle.net/10525/2170
Title: Large Distinct Part Sizes in a Random Integer Partition<br/><br/>Authors: Mutafchiev, Ljuben<br/><br/>Abstract: A partition of a positive integer n is a way of writing it as the sum of positive integerswithout 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 formulaof Hardy and Ramanujan [5]. We shall introduce the uniform probability measure P onthe set of all partitions of n assuming that the probability 1/p(n) is assigned to eachn-partition. The symbols E and V ar will be further used to denote the expectation andvariance with respect to the measure P . Thus, each conceivable numerical characteristicof the parts in a partition can be regarded as a random variable.The Maximal Number of Particles in a Branching Process with State-Dependent Immigration
http://hdl.handle.net/10525/2169
Title: The Maximal Number of Particles in a Branching Process with State-Dependent Immigration<br/><br/>Authors: Mitov, Kosto<br/><br/>Abstract: The limiting behavior of the maximal number of particles in the first n generations of a Bienaymé-Galton-Watson branching process with immigration in the state zero is studied.<br/><br/>Description: AMS subject classification: 60J80, 60J15.On some Sufficient Conditions for High Breakdown Point of ML Estimators
http://hdl.handle.net/10525/2168
Title: On some Sufficient Conditions for High Breakdown Point of ML Estimators<br/><br/>Authors: Marintcheva, Maya<br/><br/>Abstract: High breakdown point estimators LME(k) and LT E(k) for location and scale areobtained for symmetrical exponentially decreasing density family.A Characterization of the Negative Binomial Distribution
http://hdl.handle.net/10525/2167
Title: A Characterization of the Negative Binomial Distribution<br/><br/>Authors: Kolev, Nikolay; Minkova, Leda<br/><br/>Abstract: Only a few characterizations have been obtained in literatute for the negative binomial distribution (see Johnson et al., Chap. 5, 1992). In this article a characterization of the negative binomial distribution related to random sums is obtained which is motivated by the geometric distribution characterization given by Khalil et al. (1991). An interpretation in terms of an unreliable system is given.Statistical Numerical Methods for Eigenvalue Problem. Parallel Implementation
http://hdl.handle.net/10525/2166
Title: Statistical Numerical Methods for Eigenvalue Problem. Parallel Implementation<br/><br/>Authors: Dimov, Ivan; Karaivanova, Aneta<br/><br/>Abstract: The problem of evaluating the smallest eigenvalue of real symmetric matrices using statistical numerical methods is considered.<br/><br/>Description: MSC subject classification: 65C05, 65U05.Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation
http://hdl.handle.net/10525/2165
Title: Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation<br/><br/>Authors: Dimov, Ivan; Gurov, Todor<br/><br/>Abstract: 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.Making Multiple Decisions Adaptively
http://hdl.handle.net/10525/2164
Title: Making Multiple Decisions Adaptively<br/><br/>Authors: Rukhin, Andrew<br/><br/>Abstract: The asymptotic behavior of multiple decision procedures is studied when the underlying distributions depend on an unknown nuisance parameter. An adaptiveprocedure must be asymptotically optimal for each value of this nuisance parameter, and it should not depend on its value. A necessary and sufficient condition forthe existence of such a procedure is derived. Several examples are investigated indetail, and possible lack of adaptation of the traditional overall maximum likelihoodrule is discussed.Asymptotic Behaviour of a Supercritical Galton-Watson Process with Controlled Binomial Migration
http://hdl.handle.net/10525/2163
Title: Asymptotic Behaviour of a Supercritical Galton-Watson Process with Controlled Binomial Migration<br/><br/>Authors: Jacob, Christine<br/><br/>Abstract: This paper considers a branching process generated by an offspring distribution.<br/><br/>Description: AMS subject classification: 60J80, 62F12, 62P10.Monte Carlo Algorithms for Linear Problems
http://hdl.handle.net/10525/2162
Title: Monte Carlo Algorithms for Linear Problems<br/><br/>Authors: Dimov, Ivan<br/><br/>Abstract: Monte Carlo methods are a powerful tool in many fields of mathematics, physics and engineering. It is known, that these methods give statistical estimates for the functional of the solution by performing random sampling of a certain chance variable whose mathematical expectation is the desired functional. Monte Carlo methods are methods for solving problems using random variables. In the book [16] edited by Yu. A. Shreider one can find the following definition of the Monte Carlo method.<br/><br/>Description: MSC Subject Classification: 65C05, 65U05.Scaling and Multiscaling Exponents in Networks and Flows
http://hdl.handle.net/10525/2161
Title: Scaling and Multiscaling Exponents in Networks and Flows<br/><br/>Authors: Waymire, Edward<br/><br/>Abstract: The main focus of this paper is on mathematical theory and methods which have a direct bearing on problems involving multiscale phenomena. Modern technology is refiningmeasurement and data collection to spatio-temporal scales on which observed geophysical phenomena are displayed as intrinsically highly variable and intermittant heirarchicalstructures,e.g. rainfall, turbulence, etc. The heirarchical structure is reflected in the occurence of a natural separation of scales which collectively manifest at some basic unitscale. Thus proper data analysis and inference require a mathematical framework whichcouples the variability over multiple decades of scale in which basic theoretical benchmarks can be identified and calculated. This continues the main theme of the researchin this area of applied probability over the past twenty years.Large Deviations and Branching Processes
http://hdl.handle.net/10525/2160
Title: Large Deviations and Branching Processes<br/><br/>Authors: Rouault, Alain<br/><br/>Abstract: These lecture notes are devoted to present several uses of Large Deviation asymptotics in Branching Processes.Algorithmic Methods in Queues and in the Exploration of Point Processes
http://hdl.handle.net/10525/2159
Title: Algorithmic Methods in Queues and in the Exploration of Point Processes<br/><br/>Authors: Neuts, Marcel<br/><br/>Abstract: This is a review of methodology for the algorithmic study of some useful modelsin point process and queueing theory, as discussed in three lectures at the SummerInstitute at Sozopol, Bulgaria. We provide references to sources where the extensivedetails of this work are found. For future investigation, some open problems andnew methodological approaches are proposed.