Measure-Valued Processes, Stochastic Partial Differential Equations and Interacting Systems: (CRM Proceedings & Lecture Notes)

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.

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