An Introduction To Superprocesses

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An Introduction To Superprocesses

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Author : Alison Etheridge
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

An Introduction To Superprocesses written by Alison Etheridge and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

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 Yet no one approach superseded any others.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.

Measure Valued Branching Markov Processes

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Author : Zenghu Li
language : en
Publisher: Springer Nature
Release Date : 2023-03-13

Measure Valued Branching Markov Processes written by Zenghu Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-13 with Mathematics categories.

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.

Lectures On Probability Theory And Statistics

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Author : Erwin Bolthausen
language : en
Publisher: Springer
Release Date : 2004-06-04

Lectures On Probability Theory And Statistics written by Erwin Bolthausen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-04 with Mathematics categories.

This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during the period 8th-24th July, 1999. We thank the authors for all the hard work they accomplished. Their lectures are a work of reference in their domain. The School brought together 85 participants, 31 of whom gave a lecture concerning their research work. At the end of this volume you will find the list of participants and their papers. Finally, to facilitate research concerning previous schools we give here the number of the volume of "Lecture Notes" where they can be found: Lecture Notes in Mathematics 1975: n ° 539- 1971: n ° 307- 1973: n ° 390- 1974: n ° 480- 1979: n ° 876- 1976: n ° 598- 1977: n ° 678- 1978: n ° 774- 1980: n ° 929- 1981: n ° 976- 1982: n ° 1097- 1983: n ° 1117- 1988: n ° 1427- 1984: n ° 1180- 1985-1986 et 1987: n ° 1362- 1989: n ° 1464- 1990: n ° 1527- 1991: n ° 1541- 1992: n ° 1581- 1993: n ° 1608- 1994: n ° 1648- 1995: n ° 1690- 1996: n ° 1665- 1997: n ° 1717- 1998: n ° 1738- Lecture Notes in Statistics 1971: n ° 307- Table of Contents Part I Erwin Bolthausen: Large Deviations and Interacting Random Walks 1 On the construction of the three-dimensional polymer measure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Self-attracting random walks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3 One-dimensional pinning-depinning transitions. . . . . . . . . . . 105 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

S Minaire De Probabilit S Xlvi

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Author : Catherine Donati-Martin
language : en
Publisher: Springer
Release Date : 2014-12-29

S Minaire De Probabilit S Xlvi written by Catherine Donati-Martin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-29 with Mathematics categories.

Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.

Three Classes Of Nonlinear Stochastic Partial Differential Equations

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Author : Jie Xiong
language : en
Publisher: World Scientific
Release Date : 2013-05-06

Three Classes Of Nonlinear Stochastic Partial Differential Equations written by Jie Xiong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-06 with Mathematics categories.

The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs.

Fractal Geometry And Stochastics Iv

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Author : Christoph Bandt
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-08

Fractal Geometry And Stochastics Iv written by Christoph Bandt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-08 with Mathematics categories.

Over the last fifteen years fractal geometry has established itself as a substantial mathematical theory in its own right. The interplay between fractal geometry, analysis and stochastics has highly influenced recent developments in mathematical modeling of complicated structures. This process has been forced by problems in these areas related to applications in statistical physics, biomathematics and finance. This book is a collection of survey articles covering many of the most recent developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals. The authors were the keynote speakers at the conference "Fractal Geometry and Stochastics IV" at Greifswald in September 2008.

Progress In High Dimensional Percolation And Random Graphs

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Author : Markus Heydenreich
language : en
Publisher: Springer
Release Date : 2017-11-22

Progress In High Dimensional Percolation And Random Graphs written by Markus Heydenreich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4–9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dime nsional percolation. Part III, consisting of Chapters 10–13, describes recent progress in high-dimensional percolation. Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14–16, features related models and further open problems, with a focus on the big picture.

Random Measures Theory And Applications

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Author : Olav Kallenberg
language : en
Publisher: Springer
Release Date : 2017-04-12

Random Measures Theory And Applications written by Olav Kallenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-12 with Mathematics categories.

Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.

The Dynkin Festschrift

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Author : Mark I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Dynkin Festschrift written by Mark I. Freidlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Onishchik, A. A. Kirillov, and E. B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of one-dimensional probability distributions admitting non-trivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes. He created the fundamental concept of a Markov process as a family of measures corresponding to var ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A.

Combinatorial Stochastic Processes

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Author : Jim Pitman
language : en
Publisher: Springer
Release Date : 2006-07-21

Combinatorial Stochastic Processes written by Jim Pitman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-21 with Mathematics categories.

The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.