Author: David P. HarringtonPublisher:
ISBN:
Category :
Languages : en
Pages : 104
Book Description
Statistical problems for markov branching processes with random environments
Author: David P. HarringtonWorkshop on Branching Processes and Their Applications
Author: Miguel GonzálezPublisher: Springer Science & Business Media
ISBN: 3642111564
Category : Mathematics
Languages : en
Pages : 304
Book Description
One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; in other words, what Plato might have called the pure idea behind demography, population biology, cell kinetics, molecular replication, or nuclear ?ssion, had he known these scienti?c ?elds. Even in the performance of algorithms for sorting and classi?cation there is an inkling of the same pattern. In special cases, general properties of the abstract ideal then interact with the physical or biological or whatever properties at hand. But the population, or bran- ing, pattern is strong; it tends to dominate, and here lies the reason for the extreme usefulness of branching processes in diverse applications. Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.
Spatial Branching In Random Environments And With Interaction
Author: Janos EnglanderPublisher: World Scientific
ISBN: 9814569852
Category : Mathematics
Languages : en
Pages : 286
Book Description
This unique volume discusses some recent developments in the theory of spatial branching processes and superprocesses, with special emphasis on spines, Laws of Large Numbers, interactions and random media.Although this book is mainly written for mathematicians, the models discussed are relevant to certain models in population biology, and are thus hopefully interesting to the applied mathematician/biologist as well.The necessary background material in probability and analysis is provided in a comprehensive introductory chapter. Historical notes and several exercises are provided to complement each chapter.
Discrete Time Branching Processes in Random Environment
Author: Götz KerstingPublisher: John Wiley & Sons
ISBN: 1119473772
Category : Mathematics
Languages : en
Pages : 312
Book Description
Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
Branching Processes and Their Applications
Author: Inés M. del PuertoPublisher: Springer
ISBN: 3319316419
Category : Mathematics
Languages : en
Pages : 331
Book Description
This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm). The papers address a broad range of theoretical and practical aspects of branching process theory. Further, they amply demonstrate that the theoretical research in this area remains vital and topical, as well as the relevance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Biology, Genetics, and, of course, Population Dynamics. The topics covered can broadly be classified into the following areas: 1. Coalescent Branching Processes 2. Branching Random Walks 3. Population Growth Models in Varying and Random Environments 4. Size/Density/Resource-Dependent Branching Models 5. Age-Dependent Branching Models 6. Special Branching Models 7. Applications in Epidemiology 8. Applications in Biology and Genetics Offering a valuable reference guide to contemporary branching process theory, the book also explores many open problems, paving the way for future research.
Multitype Branching Processes in Random Environments
Author: Edward Wells WeissnerPublisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 124
Book Description
Consider the k-type Galton-Watson process. The work removes the restrictive assumption that particles of the same type always divide in accordance with the same probability generating function (p.g.f.). Instead, it is assumed that at each unit of time, Nature chooses a k-vector of p.g.f.s from a class of k-vectors of p.g.f.s., independently of the population, past and present, and the previously selected k-vectors, which is then assigned to the present population. Each particle of the present population then splits or disintegrates, independently of the others, in accordance with the p.g.f. assigned to its classification. This process is called a multitype branching process in a random environment (MBPRE). The work gives some necessary and some sufficient conditions for almost certain extinction of the MBPRE when there are at least two particle classifications. To obtain these results, Jensen's inequality, the dual process suggested by Smith and Wilkinson, and some results on products of random matrices are used. Since the theorems require the user to evaluate limits of sequences of products of random arrays, some corollaries are included which involve simpler, albeit less general, conditions. (Author).
Estimation problems for markov branching processes
Author: David P. HarringtonRandom Motions in Markov and Semi-Markov Random Environments 1
Author: Anatoliy PogoruiPublisher: John Wiley & Sons
ISBN: 178630547X
Category : Mathematics
Languages : en
Pages : 256
Book Description
This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented. The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.
The Imbedding Problem for Markov Branching Processes
Author: Søren JohansenRandom Motions in Markov and Semi-Markov Random Environments 2
Author: Anatoliy PogoruiPublisher: John Wiley & Sons
ISBN: 1786307065
Category : Mathematics
Languages : en
Pages : 224
Book Description
This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volume 1 to higher dimensions. It presents new results on the random motion of the realistic three-dimensional case, which has so far been barely mentioned in the literature, and deals with the interaction of particles in Markov and semi-Markov media, which has, in contrast, been a topic of intense study. The second part contains applications of Markov and semi-Markov motions in mathematical finance. It includes applications of telegraph processes in modeling stock price dynamics and investigates the pricing of variance, volatility, covariance and correlation swaps with Markov volatility and the same pricing swaps with semi-Markov volatilities.