Measure Valued Branching Markov Processes

Author by : Zenghu Li
Language : en
Publisher by : Springer Science & Business Media
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Description : Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigration superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups. The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.


An Introduction To Branching Measure Valued Processes

Author by : Evgeniĭ Borisovich Dynkin
Language : en
Publisher by : American Mathematical Soc.
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Description : For about half a century, two classes of stochastic processes--Gaussian processes and processes with independent increments--have played an important role in the development of stochastic analysis and its applications. During the last decade, a third class--branching measure-valued (BMV) processes--has also been the subject of much research. A common feature of all three classes is that their finite-dimensional distributions are infinitely divisible, allowing the use of the powerful analytic tool of Laplace (or Fourier) transforms. All three classes, in an infinite-dimensional setting, provide means for study of physical systems with infinitely many degrees of freedom. This is the first monograph devoted to the theory of BMV processes. Dynkin first constructs a large class of BMV processes, called superprocesses, by passing to the limit from branching particle systems. Then he proves that, under certain restrictions, a general BMV process is a superprocess. A special chapter is devoted to the connections between superprocesses and a class of nonlinear partial differential equations recently discovered by Dynkin.


Measure Valued Branching Processes

Author by : Donald Andrew Dawson
Language : en
Publisher by :
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Total Read : 37
Total Download : 912
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Description :


Measure Valued Processes Stochastic Partial Differential Equations And Interacting Systems

Author by : Donald Andrew Dawson
Language : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 78
Total Download : 697
File Size : 50,8 Mb
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Description : 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.


On The Martingale Problem For Interactive Measure Valued Branching Diffusions

Author by : Edwin Arend Perkins
Language : en
Publisher by : American Mathematical Soc.
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Description : This book develops stochastic integration with respect to ``Brownian trees'' and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.


An Introduction To Superprocesses

Author by : Alison Etheridge
Language : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 26
Total Download : 320
File Size : 43,7 Mb
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Description : 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.


Complex Analysis And Potential Theory

Author by : Andre Boivin
Language : en
Publisher by : American Mathematical Soc.
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Total Read : 98
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File Size : 47,6 Mb
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Description : This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.


Fractal Geometry And Stochastics Iv

Author by : Christoph Bandt
Language : en
Publisher by : Springer Science & Business Media
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Total Read : 72
Total Download : 845
File Size : 45,5 Mb
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Description : 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.


Classical And Modern Branching Processes

Author by : Krishna B. Athreya
Language : en
Publisher by : Springer Science & Business Media
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Description : This IMA Volume in Mathematics and its Applications CLASSICAL AND MODERN BRANCHING PROCESSES is based on the proceedings with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Krishna B. Athreya and Peter J agers for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE The IMA workshop on Classical and Modern Branching Processes was held during June 13-171994 as part of the IMA year on Emerging Appli cations of Probability. The organizers of the year long program identified branching processes as one of the active areas in which a workshop should be held. Krish na B. Athreya and Peter Jagers were asked to organize this. The topics covered by the workshop could broadly be divided into the following areas: 1. Tree structures and branching processes; 2. Branching random walks; 3. Measure valued branching processes; 4. Branching with dependence; 5. Large deviations in branching processes; 6. Classical branching processes.


Spatial Branching Processes Random Snakes And Partial Differential Equations

Author by : Jean-Francois Le Gall
Language : en
Publisher by : Birkhäuser
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Total Read : 31
Total Download : 415
File Size : 49,7 Mb
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Description : 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.