Spatial Branching Processes Random Snakes And Partial Differential Equations
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Spatial Branching Processes Random Snakes And Partial Differential Equations
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Author : Jean-Francois Le Gall
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-07-01
Spatial Branching Processes Random Snakes And Partial Differential Equations written by Jean-Francois Le Gall 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 1999-07-01 with Mathematics categories.
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.
Spatial Branching Processes Random Snakes And Partial Differential Equations
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Author : Jean-Francois Le Gall
language : en
Publisher:
Release Date : 1999-07-01
Spatial Branching Processes Random Snakes And Partial Differential Equations written by Jean-Francois Le Gall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-01 with categories.
Spatial Branching Processes Random Snakes And Partial Differential Equations
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Author : Jean-Francois Le Gall
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Spatial Branching Processes Random Snakes And Partial Differential Equations written by Jean-Francois Le Gall and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In these lectures, we give an account of certain recent developments of the theory of spatial branching processes. These developments lead to several fas cinating probabilistic objects, which combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial dif ferential equations. Our first objective is to give a short self-contained presentation of the measure valued branching processes called superprocesses, which have been studied extensively in the last twelve years. We then want to specialize to the important class of superprocesses with quadratic branching mechanism and to explain how a concrete and powerful representation of these processes can be given in terms of the path-valued process called the Brownian snake. To understand this representation as well as to apply it, one needs to derive some remarkable properties of branching trees embedded in linear Brownian motion, which are of independent interest. A nice application of these developments is a simple construction of the random measure called ISE, which was proposed by Aldous as a tree-based model for random distribution of mass and seems to play an important role in asymptotics of certain models of statistical mechanics. We use the Brownian snake approach to investigate connections between super processes and partial differential equations. These connections are remarkable in the sense that almost every important probabilistic question corresponds to a significant analytic problem.
A Minicourse On Stochastic Partial Differential Equations
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Author : Robert C. Dalang
language : en
Publisher: Springer Science & Business Media
Release Date : 2009
A Minicourse On Stochastic Partial Differential Equations written by Robert C. Dalang 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 2009 with Mathematics categories.
This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.
Perspectives In Nonlinear Partial Differential Equations
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Author : Henri Berestycki
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Perspectives In Nonlinear Partial Differential Equations written by Henri Berestycki 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 2007 with Mathematics categories.
In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.
Surveys In Stochastic Processes
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Author : Jochen Blath
language : en
Publisher: European Mathematical Society
Release Date : 2011
Surveys In Stochastic Processes written by Jochen Blath and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The 33rd Bernoulli Society Conference on Stochastic Processes and Their Applications was held in Berlin from July 27 to July 31, 2009. It brought together more than 600 researchers from 49 countries to discuss recent progress in the mathematical research related to stochastic processes, with applications ranging from biology to statistical mechanics, finance and climatology. This book collects survey articles highlighting new trends and focal points in the area written by plenary speakers of the conference, all of them outstanding international experts. A particular aim of this collection is to inspire young scientists to pursue research goals in the wide range of fields represented in this volume.
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.
Three Classes Of Nonlinear Stochastic Partial Differential Equations
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Author : Jie Xiong
language : en
Publisher: World Scientific
Release Date : 2013
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 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.
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.
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.