On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
On the Martingale Problem for Interactive Measure-Valued Branching Diffusions

Author: Edwin Arend Perkins

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 102

ISBN-13: 0821803581

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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.

Stochastic Partial Differential Equations: Six Perspectives
Stochastic Partial Differential Equations: Six Perspectives

Author: René Carmona

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 360

ISBN-13: 9780821808061

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Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR

Measure-valued Processes, Stochastic Partial Differential Equations, and Interacting Systems
Measure-valued Processes, Stochastic Partial Differential Equations, and Interacting Systems

Author: Donald Andrew Dawson

Publisher: American Mathematical Soc.

Published: 1994-01-01

Total Pages: 260

ISBN-13: 9780821870440

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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.

Perplexing Problems in Probability
Perplexing Problems in Probability

Author: Maury Bramson

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 393

ISBN-13: 1461221684

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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.

Seminaire de Probabilites XXIX
Seminaire de Probabilites XXIX

Author: Jacques Azema

Publisher: Springer

Published: 2006-11-14

Total Pages: 337

ISBN-13: 354044744X

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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.

Stochastic Ordinary and Stochastic Partial Differential Equations
Stochastic Ordinary and Stochastic Partial Differential Equations

Author: Peter Kotelenez

Publisher: Springer Science & Business Media

Published: 2007-12-05

Total Pages: 452

ISBN-13: 0387743170

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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.

Decision Problems for Equational Theories of Relation Algebras
Decision Problems for Equational Theories of Relation Algebras

Author: H. Andréka

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 146

ISBN-13: 0821805959

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"We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract.