CRM Proceedings & Lecture Notes 1994; 241 pp Volume: 5 ISBN10: 0821869922 ISBN13: 9780821869925 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 measurevalued 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 measurevalued 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 FlemingViot 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 copublished with the Centre de Recherches Mathématiques. Readership Researchers and graduate students in probability and stochastic processes who have an interest in learning about stochastic partial differential equations, superprocesses, and interacting systems. Table of Contents  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 longrange contact process, and its phase transition
 L. Overbeck  Some aspects of the Martin boundary of measurevalued diffusions
 B. A. Schmuland  A Dirichlet form primer
 T. Shiga  Stationary distribution problem for interacting diffusion systems
 A. Stoeckl and A. Wakolbinger  On clanrecurrence 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 measurevalued processes
