Discrete Time Branching Processes In Random Environment
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| Author | : Götz Kersting |
| Publisher | : John Wiley & Sons |
| Total Pages | : 306 |
| Release | : 2017-11-29 |
| Genre | : Mathematics |
| ISBN | : 1786302527 |
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.
| Author | : Kersting Gotz |
| Publisher | : Iste Press - Elsevier |
| Total Pages | : 250 |
| Release | : 2017-10-01 |
| Genre | : |
| ISBN | : 9781785482427 |
There are several books devoted to the theory of branching processes. However, the theory of branching processes in random environment is rather pour reflected in these books. During the last two decades an essential progress was achieved on this field in particular, owing to the efforts of the authors of the proposal. We develop in this book a unique and new approach to study branching processes in random environment To compare properties of branching processes in random environment with properties of ordinary random walks This approach, combined with the properties of random walks conditioned to stay nonnegative or negative allows to find the probability of survival of the critical and subcritical branching processes in random environment as well as Yaglom-type limit theorems for the mentioned classes of processes
| Author | : Patsy Haccou |
| Publisher | : Cambridge University Press |
| Total Pages | : 342 |
| Release | : 2005-05-19 |
| Genre | : Mathematics |
| ISBN | : 9780521832205 |
This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
| Author | : Anatoliy Pogorui |
| Publisher | : John Wiley & Sons |
| Total Pages | : 224 |
| Release | : 2021-01-11 |
| Genre | : Mathematics |
| ISBN | : 1119808170 |
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.
| Author | : Anatoliy Pogorui |
| Publisher | : John Wiley & Sons |
| Total Pages | : 256 |
| Release | : 2021-01-12 |
| Genre | : Mathematics |
| ISBN | : 1119808189 |
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.
| Author | : Ibrahim Rahimov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 207 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461242169 |
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
| Author | : C.C. Heyde |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 189 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461225582 |
This volume presents the edited proceedings of the First World Congress on Branching Processes. The contributions present new research and surveys of the current research activity in this field. As a result, all those undertaking research in the subject will find this a timely and high-quality volume to have on their shelves.
| Author | : David Louis Tanny |
| Publisher | : |
| Total Pages | : 306 |
| Release | : 1975 |
| Genre | : Distribution (Probability theory) |
| ISBN | : |
| Author | : Linda J. S. Allen |
| Publisher | : Springer |
| Total Pages | : 55 |
| Release | : 2015-08-20 |
| Genre | : Mathematics |
| ISBN | : 331921554X |
This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics at Texas Tech University, USA.
| Author | : D N Shanbhag |
| Publisher | : Gulf Professional Publishing |
| Total Pages | : 1028 |
| Release | : 2003-02-24 |
| Genre | : Computers |
| ISBN | : 9780444500137 |
This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.
