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It is known that certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments have diffusive scaling limits. Here, in the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was first developed by Le Jan and Raimond, who showed that each such flow is characterized by its -point motions. The authors' work focuses on a class of stochastic flows of kernels with Brownian -point motions which, after their inventors, will be called Howitt-Warren flows. The authors' main result gives a graphical construction of general Howitt-Warren flows, where the underlying random environment takes on the form of a suitably marked Brownian web. This extends earlier work of Howitt and Warren who showed that a special case, the so-called "erosion flow", can be constructed from two coupled "sticky Brownian webs". The authors' construction for general Howitt-Warren flows is based on a Poisson marking procedure developed by Newman, Ravishankar and Schertzer for the Brownian web. Alternatively, the authors show that a special subclass of the Howitt-Warren flows can be constructed as random flows of mass in a Brownian net, introduced by Sun and Swart. Using these constructions, the authors prove some new results for the Howitt-Warren flows.
Here is easy reference to a wealth of facts and formulae associated with Brownian motion, collecting in one volume more than 2500 numbered formulae. The book serves as a basic reference for researchers, graduate students, and people doing applied work with Brownian motion and diffusions, and can be used as a source of explicit examples when teaching stochastic processes.
Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.
This volume is dedicated to the memory of Marc Yor, who passed away in 2014. The invited contributions by his collaborators and former students bear testament to the value and diversity of his work and of his research focus, which covered broad areas of probability theory. The volume also provides personal recollections about him, and an article on his essential role concerning the Doeblin documents. With contributions by P. Salminen, J-Y. Yen & M. Yor; J. Warren; T. Funaki; J. Pitman& W. Tang; J-F. Le Gall; L. Alili, P. Graczyk & T. Zak; K. Yano & Y. Yano; D. Bakry & O. Zribi; A. Aksamit, T. Choulli & M. Jeanblanc; J. Pitman; J. Obloj, P. Spoida & N. Touzi; P. Biane; J. Najnudel; P. Fitzsimmons, Y. Le Jan & J. Rosen; L.C.G. Rogers & M. Duembgen; E. Azmoodeh, G. Peccati & G. Poly, timP-L Méliot, A. Nikeghbali; P. Baldi; N. Demni, A. Rouault & M. Zani; N. O'Connell; N. Ikeda & H. Matsumoto; A. Comtet & Y. Tourigny; P. Bougerol; L. Chaumont; L. Devroye & G. Letac; D. Stroock and M. Emery.
The progress of science and technology has placed Queueing Theory among the most popular disciplines in applied mathematics, operations research, and engineering. Although queueing has been on the scientific market since the beginning of this century, it is still rapidly expanding by capturing new areas in technology. Advances in Queueing provides a comprehensive overview of problems in this enormous area of science and focuses on the most significant methods recently developed. Written by a team of 24 eminent scientists, the book examines stochastic, analytic, and generic methods such as approximations, estimates and bounds, and simulation. The first chapter presents an overview of classical queueing methods from the birth of queues to the seventies. It also contains the most comprehensive bibliography of books on queueing and telecommunications to date. Each of the following chapters surveys recent methods applied to classes of queueing systems and networks followed by a discussion of open problems and future research directions. Advances in Queueing is a practical reference that allows the reader quick access to the latest methods.
This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.
This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.
The state of the art in fluid-based methods for stability analysis, giving researchers and graduate students command of the tools.
In The Economics of Inaction, leading economist Nancy Stokey shows how the tools of stochastic control can be applied to dynamic problems of decision making under uncertainty when fixed costs are present. Stokey provides a self-contained, rigorous, and clear treatment of two types of models, impulse and instantaneous control. She presents the relevant results about Brownian motion and other diffusion processes, develops methods for analyzing each type of problem, and discusses applications to price setting, investment, and durable goods purchases."--Pub. desc.