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Author : Perkins, E. A. (Edwin A.),Carleton University. Laboratory for Research in Statistics and Probability,University of Ottawa
Publisher : Laboratory for Research in Statistics and Probability, Carleton University = Laboratoire de recherche en statistique et probabilités, Carleton University
Page : 93 pages
File Size : 40,8 Mb
Release : 1993
Category : Branching processes
ISBN : OCLC:35539974
Author : Edwin Arend Perkins
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 40,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803585
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.
Author : René Carmona
Publisher : American Mathematical Soc.
Page : 349 pages
File Size : 43,8 Mb
Release : 1999
Category : Stochastic partial differential equations
ISBN : 9780821821008
The field of Stochastic Partial Differential Equations (SPDEs) is one of the most dynamically developing areas of mathematics. It lies at the cross section of probability, partial differential equations, population biology, and mathematical physics. The field is especially attractive because of its interdisciplinary nature and the enormous richness of current and potential future applications. This volume is a collection of six important topics in SPDEs presented from the viewpoint of distinguished scientists working in the field and related areas. Emphasized are the genesis and applications of SPDEs as well as mathematical theory and numerical methods. .
Author : Donald Andrew Dawson
Publisher : American Mathematical Soc.
Page : 260 pages
File Size : 46,6 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 0821870440
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.
Author : Maury Bramson,Richard T. Durrett
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461221685
Harry Kesten has had a profound influence on probability theory for over 30 years. To honour his achievements a number of prominent probabilists have written survey articles on a wide variety of active areas of contemporary probability, many of which are closely related to Kesten's work.
Author : Takeyuki Hida,Kimiaki Saito
Publisher : World Scientific
Page : 240 pages
File Size : 52,9 Mb
Release : 1999-08-16
Category : Science
ISBN : 9789814543606
Author : Jacques Azema,Michel Emery,Paul-Andre Meyer,Marc Yor
Publisher : Springer
Page : 337 pages
File Size : 41,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540447443
All the papers included in this volume are original research papers. They represent an important part of the work of French probabilists and colleagues with whom they are in close contact throughout the world. The main topics of the papers are martingale and Markov processes studies.
Author : Peter Kotelenez
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 47,9 Mb
Release : 2007-12-05
Category : Mathematics
ISBN : 9780387743172
Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.
Author : H. Andréka,Steven R. Givant,I. Németi
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 48,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805954
This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.
Author : Raúl E. Curto,Lawrence A. Fialkow
Publisher : American Mathematical Soc.
Page : 52 pages
File Size : 45,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804858
In this book, the authors introduce a matricial approach to the truncated complex moment problem and apply it to the case of moment matrices of flat data type, for which the columns corresponding to the homogeneous monomials in $z$ and $\bar z$ of highest degree can be written in terms of monomials of lower degree. Necessary and sufficient conditions for the existence and uniqueness of representing measures are obtained in terms of positivity and extension criteria for moment matrices.
Author : Ole H. Hald,Joyce McLaughlin
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 51,9 Mb
Release : 1996
Category : Asymptotic distribution
ISBN : 9780821804865
In this paper we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We show that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is shown which, when the additive constant is given, yields an approximation to the potential at a dense set of points. We present an estimate for the error made by the formula. A substantial part of this work is the derivation of the asymptotic forms for a rich set of eigenvalues and eigenfunctions for a large set of rectangles.
Author : Zenghu Li
Publisher : Springer Nature
Page : 481 pages
File Size : 40,7 Mb
Release : 2023-04-14
Category : Mathematics
ISBN : 9783662669105
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.
Author : Liviu I. Nicolaescu
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 53,6 Mb
Release : 1997
Category : Geometry, Differential
ISBN : 9780821806210
In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.
Author : Moshé Flato,Jacques Charles Henri Simon,Erik Taflin
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 51,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806838
The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations. These equations govern first quantized electrodynamics and are the starting point for a rigorous formulation of quantum electrodynamics. The presentation is given within the formalism of nonlinear group and Lie algebra representations, i.e. the powerful new approach to nonlinear evolution equations covariant under a group action. The authors prove that the nonlinear Lie algebra representation given by the manifestly covariant Maxwell-Dirac equations is integrable to a global nonlinear representation of the Poincare group on a differentiable manifold of small initial conditions. This solves, in particular, the small-data Cauchy problem for the Maxwell-Dirac equations globally in time. The existence of modified wave operators and asymptotic completeness is proved. The asymptotic representations (at infinite time) turn out to be nonlinear. A cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the infrared tail of the electron are developed.
Author : Darryl McCullough,Andy Miller
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 53,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804599
This memoir examines the automorphism group of a group $G$ with a fixed free product decomposition $G_1*\cdots *G_n$. An automorphism is called symmetric if it carries each factor $G_i$ to a conjugate of a (possibly different) factor $G_j$. The symmetric automorphisms form a group $\Sigma Aut(G)$ which contains the inner automorphism group $Inn(G)$. The quotient $\Sigma Aut(G)/Inn(G)$ is the symmetric outer automorphism group $\Sigma Out(G)$, a subgroup of $Out(G)$. It coincides with $Out(G)$ if the $G_i$ are indecomposable and none of them is infinite cyclic. To study $\Sigma Out(G)$, the authors construct an $(n-2)$-dimensional simplicial complex $K(G)$ which admits a simplicial action of $Out(G)$. The stabilizer of one of its components is $\Sigma Out(G)$, and the quotient is a finite complex. The authors prove that each component of $K(G)$ is contractible and describe the vertex stabilizers as elementary constructs involving the groups $G_i$ and $Aut(G_i)$. From this information, two new structural descriptions of $\Sigma Aut (G)$ are obtained. One identifies a normal subgroup in $\Sigma Aut(G)$ of cohomological dimension $(n-1)$ and describes its quotient group, and the other presents $\Sigma Aut (G)$ as an amalgam of some vertex stabilizers. Other applications concern torsion and homological finiteness properties of $\Sigma Out (G)$ and give information about finite groups of symmetric automorphisms. The complex $K(G)$ is shown to be equivariantly homotopy equivalent to a space of $G$-actions on $\mathbb R$-trees, although a simplicial topology rather than the Gromov topology must be used on the space of actions.
