Download or read book Measure Valued Branching Markov Processes written by Zenghu Li and published by Springer Nature. This book was released on 2023-04-14 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a compact introduction to the theory of measure-valued branching processes, immigration processes and Ornstein–Uhlenbeck type processes. Measure-valued branching processes arise as high density limits of branching particle systems. The first part of the book gives an analytic construction of a special class of such processes, the Dawson–Watanabe superprocesses, which includes the finite-dimensional continuous-state branching process as an example. Under natural assumptions, it is shown that the superprocesses have Borel right realizations. Transformations are then used to derive the existence and regularity of several different forms of the superprocesses. This technique simplifies the constructions and gives useful new perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The second part investigates immigration structures associated with the measure-valued branching processes. The structures are formulated by skew convolution semigroups, which are characterized in terms of infinitely divisible probability entrance laws. A theory of stochastic equations for one-dimensional continuous-state branching processes with or without immigration is developed, which plays a key role in the construction of measure flows of those processes. The third part of the book studies a class of Ornstein-Uhlenbeck type processes in Hilbert spaces defined by generalized Mehler semigroups, which arise naturally in fluctuation limit theorems of the immigration superprocesses. This volume is aimed at researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.
Download or read book An Introduction to Superprocesses written by Alison Etheridge and published by American Mathematical Soc.. This book was released on 2000 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 20 years, the study of superprocesses has expanded into a major industry and can now be regarded as a central theme in modern probability theory. This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis. A variety of different approaches to the superprocesses emerged over the last ten years. Yet no one approach superseded any others. In this book, readers are exposed to a number of different ways of thinking about the processes, and each is used to motivate some key results. The emphasis is on why results are true rather than on rigorous proof. Specific results are given, including extensive references to current literature for their general form.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Branching Processes written by Krishna B. Athreya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to the Theory of Point Processes written by D.J. Daley and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.
Download or read book An Introduction to the Theory of Point Processes written by Daryl J. Daley and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic point processes are sets of randomly located points in time, on the plane or in some general space. This book provides a general introduction to the theory, starting with simple examples and an historical overview, and proceeding to the general theory. It thoroughly covers recent work in a broad historical perspective in an attempt to provide a wider audience with insights into recent theoretical developments. It contains numerous examples and exercises. This book aims to bridge the gap between informal treatments concerned with applications and highly abstract theoretical treatments.
Download or read book Spatial Branching Processes Random Snakes and Partial Differential Equations written by Jean-Francois Le Gall and published by Birkhäuser. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Measure valued Processes Stochastic Partial Differential Equations and Interacting Systems written by Donald Andrew Dawson and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this collection explore the connections between the rapidly developing fields of measure-valued processes, stochastic partial differential equations, and interacting particle systems, each of which has undergone profound development in recent years. Bringing together ideas and tools arising from these different sources, the papers include contributions to major directions of research in these fields, explore the interface between them, and describe newly developing research problems and methodologies. Several papers are devoted to different aspects of measure-valued branching processes (also called superprocesses). Some new classes of these processes are described, including branching in catalytic media, branching with change of mass, and multilevel branching. Sample path and spatial clumping properties of superprocesses are also studied. The papers on Fleming-Viot processes arising in population genetics include discussions of the role of genealogical structures and the application of the Dirichlet form methodology. Several papers are devoted to particle systems studied in statistical physics and to stochastic partial differential equations which arise as hydrodynamic limits of such systems. With overview articles on some of the important new developments in these areas, this book would be an ideal source for an advanced graduate course on superprocesses.
Download or read book Stochastic Partial Differential Equations written by Alison Etheridge and published by Cambridge University Press. This book was released on 1995-07-13 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consists of papers given at the ICMS meeting held in 1994 on this topic, and brings together some of the world's best known authorities on stochastic partial differential equations.
Download or read book The Poisson Dirichlet Distribution and Related Topics written by Shui Feng and published by Springer Science & Business Media. This book was released on 2010-05-27 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a comprehensive study of the Poisson-Dirichlet distribution, this volume emphasizes recent progress in evolutionary dynamics and asymptotic behaviors. The self-contained text presents methods and techniques that appeal to researchers in a wide variety of subjects.
Download or read book Measure valued Branching Processes written by Donald Andrew Dawson and published by Department of Mathematics and Statistics, Carleton University. This book was released on 1982 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Seminar on Stochastic Processes 1992 written by Cinlar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1992 Seminar on Stochastic Processes was held at the Univer sity of Washington from March 26 to March 28, 1992. This was the twelfth in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, University of Florida, University of Virginia, University of California, San Diego, University of British Columbia and University of California, Los An geles. Following the successful format of previous years, there were five invited lectures, delivered by R. Adler, R. Banuelos, J. Pitman, S. J. Taylor and R. Williams, with the remainder of the time being devoted to informal communications and workshops on current work and problems. The enthusiasm and interest of the participants cre ated a lively and stimulating atmosphere for the seminar. A sample of the research discussed there is contained in this volume. The 1992 Seminar was made possible through the support of the National Science Foundation, the National Security Agency, the Institute of Mathematical Statistics and the University of Washing ton. We extend our thanks to them and to the publisher Birkhauser Boston for their support and encouragement. Richard F. Bass Krzysztof Burdzy Seattle, 1992 SUPERPROCESS LOCAL AND INTERSECTION LOCAL TIMES AND THEIR CORRESPONDING PARTICLE PICTURES Robert J.
Download or read book From Probability to Finance written by Ying Jiao and published by Springer Nature. This book was released on 2020-03-20 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of lecture notes of mini-courses taught at BICMR Summer School of Financial Mathematics, from May 29 to June 9, 2017. Each chapter is self-contained and corresponds to one mini-course which deals with a distinguished topic, such as branching processes, enlargement of filtrations, Hawkes processes, copula models and valuation adjustment analysis, whereas the global topics cover a wide range of advanced subjects in financial mathematics, from both theoretical and practical points of view. The authors include world-leading specialists in the domain and also young active researchers. This book will be helpful for students and those who work on probability and financial mathematics.
Download or read book Stochastic Models for Structured Populations written by Sylvie Meleard and published by Springer. This book was released on 2015-09-03 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.
Download or read book Stochastic Analysis written by Jean-Pierre Fouque and published by . This book was released on 1996 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Branching Processes written by Patsy Haccou and published by Cambridge University Press. This book was released on 2005-05-19 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt:
