Spatial Branching In Random Environments And With Interaction
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| Author | : Janos Englander |
| Publisher | : World Scientific |
| Total Pages | : 286 |
| Release | : 2014-11-20 |
| Genre | : Mathematics |
| ISBN | : 9814569852 |
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.
| Author | : Janos Englander |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 270 |
| Release | : 2015-01-19 |
| Genre | : Mathematics |
| ISBN | : 9789814569835 |
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.
| Author | : Emma Horton |
| Publisher | : Springer Nature |
| Total Pages | : 278 |
| Release | : 2023-12-17 |
| Genre | : Mathematics |
| ISBN | : 3031395468 |
This monograph highlights the connection between the theory of neutron transport and the theory of non-local branching processes. By detailing this frequently overlooked relationship, the authors provide readers an entry point into several active areas, particularly applications related to general radiation transport. Cutting-edge research published in recent years is collected here for convenient reference. Organized into two parts, the first offers a modern perspective on the relationship between the neutron branching process (NBP) and the neutron transport equation (NTE), as well as some of the core results concerning the growth and spread of mass of the NBP. The second part generalizes some of the theory put forward in the first, offering proofs in a broader context in order to show why NBPs are as malleable as they appear to be. Stochastic Neutron Transport will be a valuable resource for probabilists, and may also be of interest to numerical analysts and engineers in the field of nuclear research.
| Author | : Ole E Barndorff-nielsen |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 345 |
| Release | : 2015-05-07 |
| Genre | : Business & Economics |
| ISBN | : 9814678600 |
Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance.In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.
| Author | : Nicolas Privault |
| Publisher | : World Scientific |
| Total Pages | : 373 |
| Release | : 2021-09-02 |
| Genre | : Mathematics |
| ISBN | : 9811226628 |
This book introduces the mathematics of stochastic interest rate modeling and the pricing of related derivatives, based on a step-by-step presentation of concepts with a focus on explicit calculations. The types of interest rates considered range from short rates to forward rates such as LIBOR and swap rates, which are presented in the HJM and BGM frameworks. The pricing and hedging of interest rate and fixed income derivatives such as bond options, caps, and swaptions, are treated using forward measure techniques. An introduction to default bond pricing and an outlook on model calibration are also included as additional topics.This third edition represents a significant update on the second edition published by World Scientific in 2012. Most chapters have been reorganized and largely rewritten with additional details and supplementary solved exercises. New graphs and simulations based on market data have been included, together with the corresponding R codes.This new edition also contains 75 exercises and 4 problems with detailed solutions, making it suitable for advanced undergraduate and graduate level students.
| Author | : Jean-Francois Le Gall |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 438 |
| Release | : 1999-07-01 |
| Genre | : Mathematics |
| ISBN | : 9783764361266 |
This book introduces several remarkable new probabilistic objects that combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial differential equations (PDE). The Brownian snake approach is used to give a powerful representation of superprocesses and also to investigate connections between superprocesses and PDEs. These are notable because almost every important probabilistic question corresponds to a significant analytic problem.
| Author | : Jean-Dominique Deuschel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 443 |
| Release | : 2005-12-05 |
| Genre | : Mathematics |
| ISBN | : 3540271104 |
Core papers emanating from the research network, DFG-Schwerpunkt: Interacting stochastic systems of high complexity.
| Author | : K.S. Alexander |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 278 |
| Release | : 1991-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780817634773 |
This volume has been created in honor of the seventieth birthday of Ted Harris, which was celebrated on January 11th, 1989. The papers rep resent the wide range of subfields of probability theory in which Ted has made profound and fundamental contributions. This breadth in Ted's research complicates the task of putting together in his honor a book with a unified theme. One common thread noted was the spatial, or geometric, aspect of the phenomena Ted investigated. This volume has been organized around that theme, with papers covering four major subject areas of Ted's research: branching processes, percola tion, interacting particle systems, and stochastic flows. These four topics do not· exhaust his research interests; his major work on Markov chains is commemorated in the standard technology "Harris chain" and "Harris recurrent" . The editors would like to take this opportunity to thank the speakers at the symposium and the contributors to this volume. Their enthusi astic support is a tribute to Ted Harris. We would like to express our appreciation to Annette Mosley for her efforts in typing the manuscripts and to Arthur Ogawa for typesetting the volume. Finally, we gratefully acknowledge the National Science Foundation and the University of South ern California for their financial support.
| Author | : Donald Andrew Dawson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 492 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780821810637 |
This book presents the refereed proceedings of the International Conference on Stochastic Models held in Ottawa (ON, Canada) in honor of Professor Donald A. Dawson. Contributions to the volume were written by students and colleagues of Professor Dawson, many of whom are eminent researchers in their own right. A main theme of the book is the development and study of the Dawson-Watanabe "superprocess", a fundamental building block in modelling interaction particle systems undergoing reproduction and movement. The volume also contains an excellent review article by Professor Dawson and a complete list of his work. This comprehensive work offers a wide assortment of articles on Markov processes, branching processes, mathematical finance, filtering, queueing networks, time series, and statistics. It should be of interest to a broad mathematical audience.
| Author | : Nicolas Lanchier |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 486 |
| Release | : 2024-07-01 |
| Genre | : Mathematics |
| ISBN | : 3110791889 |
This volume provides an overview of two of the most important examples of interacting particle systems, the contact process, and the voter model, as well as their many variants introduced in the past 50 years. These stochastic processes are organized by domains of application (epidemiology, population dynamics, ecology, genetics, sociology, econophysics, game theory) along with a flavor of the mathematical techniques developed for their analysis.
