Discrete Time Branching Processes in Random Environment
Discrete Time Branching Processes in Random Environment

Author: Götz Kersting

Publisher: John Wiley & Sons

Published: 2017-11-29

Total Pages: 306

ISBN-13: 1786302527

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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 in Random Environment
Branching Processes in Random Environment

Author: Kersting Gotz

Publisher: Iste Press - Elsevier

Published: 2017-10-01

Total Pages: 250

ISBN-13: 9781785482427

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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

Controlled Branching Processes
Controlled Branching Processes

Author: Miguel González Velasco

Publisher: John Wiley & Sons

Published: 2018-03-13

Total Pages: 240

ISBN-13: 1786302535

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The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.

Branching Processes
Branching Processes

Author: Patsy Haccou

Publisher: Cambridge University Press

Published: 2005-05-19

Total Pages: 342

ISBN-13: 9780521832205

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This book covers the mathematical idea of branching processes, and tailors it for a biological audience.

Branching Processes
Branching Processes

Author: Krishna B. Athreya

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 301

ISBN-13: 3642653715

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The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.

Random Motions in Markov and Semi-Markov Random Environments 2
Random Motions in Markov and Semi-Markov Random Environments 2

Author: Anatoliy Pogorui

Publisher: John Wiley & Sons

Published: 2021-01-11

Total Pages: 224

ISBN-13: 1119808170

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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.

Random Motions in Markov and Semi-Markov Random Environments 1
Random Motions in Markov and Semi-Markov Random Environments 1

Author: Anatoliy Pogorui

Publisher: John Wiley & Sons

Published: 2021-01-12

Total Pages: 256

ISBN-13: 1119808189

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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.

Random Sums and Branching Stochastic Processes
Random Sums and Branching Stochastic Processes

Author: Ibrahim Rahimov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 207

ISBN-13: 1461242169

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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.