Journal ArticleDOI
Moment computations for subcritical branching processes
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In this paper, the authors consider methods for computing moments connected with subcritical multitype branching processes and prove simultaneously the existence of the moments by stressing the interplay between moment and cumulant structure, and they consider the kinds of moments arising in (1) times to extinction, (2) ultimate number of particles starting from a single particle, and (3) equilibrium numbers of particles for subcritical processes experiencing immigration.Abstract:
The present paper considers methods for computing moments connected with subcritical multitype branching processes. By stressing the interplay between moment and cumulant structure, it is possible to prove simultaneously the existence of the moments. The kinds of moments considered are those arising in (1) times to extinction, (2) ultimate numbers of particles starting from a single particle, and (3) equilibrium numbers of particles for subcritical processes experiencing immigration. SUBCRITICAL MULTITYPE BRANCHING PROCESS; MOMENT; CUMULANT; COMPUTATIONread more
Citations
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Journal ArticleDOI
Cumulants and partition lattices1
TL;DR: In this article, the joint cumulant of a set of random variables is defined as an alternating sum of moments with appropriate integral coefficients, and its properties are derived by exploiting properties of the Mobius function of a partition lattice.
Journal ArticleDOI
In the Garden of Branching Processes
TL;DR: The current paper surveys and develops numerical methods for Markovian multitype branching processes in continuous time and applies these methods to four models: two population genetics models, a models for vaccination against an infectious disease in a community of households, and a model for the growth of resistant HIV virus in patients undergoing drug therapy.
Posted Content
Scaling limits of random graph models at criticality: Universality and the basin of attraction of the Erdős-Rényi random graph
TL;DR: A general program for proving that for a wide class of models, under moment conditions, the nature of this emergence is universal and looks like the classical Erd\H{o}s-R\'enyi random graph, in the sense of the critical scaling window is developed.
Journal ArticleDOI
Extinction probabilities and times to extinction for populations of tsetse flies Glossina spp. (Diptera: Glossinidae) subjected to various control measures.
TL;DR: The stochastic branching process was used to derive equations for the mean and variance of the probability of, and time to, extinction in tsetse populations and the practical, economic implication for the sterile insect technique is that the low-tech methods used to suppress tsete populations should not be halted when the release of sterile males is initiated.
Journal ArticleDOI
Branching processes. I
V. A. Vatutin,A. M. Zubkov +1 more
TL;DR: The main results obtained from 1968 to 1983 in the theory of Markov branching processes and processes with transformations depending on the age of particles are reflected in this article, along with the traditional sections (integral and local theorems, stationary measures), including sections devoted to statistics of branching processes.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Book
Time Series: Data Analysis and Theory
TL;DR: This book will be most useful to applied mathematicians, communication engineers, signal processors, statisticians, and time series researchers, both applied and theoretical.
Book
The Theory of Branching Processes
TL;DR: A review of the Galton and Watson mathematical model that applies probability theory to the effects of chance on the development of populations is given in this article, followed by a systematic development of branching processes, and a brief description of some of the important applications.
Book
Real and abstract analysis
Edwin Hewitt,Karl R. Stromberg +1 more
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT, and the €(D) includes 7% for Germany, the€(A) includes 10% for Austria.