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Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems
Edited by: D. A. Dawson, The Fields Institute, Toronto, ON, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Proceedings & Lecture Notes
1994; 241 pp
Volume: 5
ISBN-10: 0-8218-6992-2
ISBN-13: 978-0-8218-6992-5
List Price: US$75 Member Price: US$60
Order Code: CRMP/5

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.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Researchers and graduate students in probability and stochastic processes who have an interest in learning about stochastic partial differential equations, superprocesses, and interacting systems.

• R. J. Adler -- Superprocesses: The particle picture
• P. H. Bezandry, R. Ferland, G. O. Giroux, and J.-C. Roberge -- Une approache probabiliste de resolution d'equations non lineaires
• K. Burdzy -- Variation of iterated Brownian motion
• J. T. Cox and A. Greven -- The finite systems scheme: An abstract theorem and a new example
• D. A. Dawson, K. J. Hochberg, and V. S. Vinogradov -- On path properties of super-$$2$$ processes. I
• E. B. Dynkin -- A type of interaction between superprocesses and branching particle systems
• S. N. Ethier and T. Shiga -- Neutral allelic genealogy
• K. Fleischmann -- Superprocesses in catalytic media
• L. G. Gorostiza -- A measure valued process arising from a branching particle system with changes of mass
• L. G. Gorostiza and A. Wakolbinger -- Long time behavior of critical branching particle systems and applications
• P. M. Kotelenez and K. Wang -- Newtonian particle mechanics and stochastic partial differential equations
• T.-Y. Lee and B. Remillard -- Occupation time limit theorems for independent random walks
• C. Leonard -- Large deviations and Boltzmann equation
• C. D. Mueller and R. Tribe -- A stochastic PDE arising as the limit of a long-range contact process, and its phase transition
• L. Overbeck -- Some aspects of the Martin boundary of measure-valued diffusions
• B. A. Schmuland -- A Dirichlet form primer
• T. Shiga -- Stationary distribution problem for interacting diffusion systems
• A. Stoeckl and A. Wakolbinger -- On clan-recurrence and -transience in time stationary branching Brownian particle systems
• H. Tanemura -- Tagged particle problem for an infinite hard core particle system in $${\mathbb R}^d$$
• Y. Wu -- A three level particle system and existence of general multilevel measure-valued processes