Constructing Nonhomeomorphic Stochastic Flows
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Constructing Nonhomeomorphic Stochastic Flows
Author: R. W. R. Darling
language: en
Publisher: American Mathematical Soc.
Release Date: 1987
The purpose of this article is the construction of stochastic flows from the finite-dimensional distributions without any smoothness assumptions. Also examines the relation between covariance functions and finite-dimensional distributions. The stochastic continuity of stochastic flows in the time parameter are proved in each section. These results give some extensions of the results obtained by Harris, by Baxendale and Harris and by other authors. In particular, the author studies coalescing flows, which were introduced by Harris for the study of flows of nonsmooth maps.
Measure-valued Processes and Stochastic Flows
Author: Andrey A. Dorogovtsev
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2023-11-06
This book discusses the systems of interacting particles evolving in the random media. The focus is on the study of both the finite subsystems motion and the flow, describing motion of all particles in the space. The integral characteristics of the system and mass distribution are also covered and results are illustrated with examples from turbulence theory, synchronization and DNA evolution.
Geometry of Random Motion
Author: Richard Durrett
language: en
Publisher: American Mathematical Soc.
Release Date: 1988
In July 1987, an AMS-IMS-SIAM Joint Summer Research Conference on Geometry of Random Motion was held at Cornell University. The initial impetus for the meeting came from the desire to further explore the now-classical connection between diffusion processes and second-order (hypo)elliptic differential operators. To accomplish this goal, the conference brought together leading researchers with varied backgrounds and interests: probabilists who have proved results in geometry, geometers who have used probabilistic methods, and probabilists who have studied diffusion processes. Focusing on the interplay between probability and differential geometry, this volume examines diffusion processes on various geometric structures, such as Riemannian manifolds, Lie groups, and symmetric spaces. Some of the articles specifically address analysis on manifolds, while others center on (nongeometric) stochastic analysis. The majority of the articles deal simultaneously with probabilistic and geometric techniques. Requiring a knowledge of the modern theory of diffusion processes, this book will appeal to mathematicians, mathematical physicists, and other researchers interested in Brownian motion, diffusion processes, Laplace-Beltrami operators, and the geometric applications of these concepts. The book provides a detailed view of the leading edge of research in this rapidly moving field.