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Markov Processes And Related Problems Of Analysis

Author: Evgeniĭ Borisovich Dynkin
Publisher: Cambridge University Press
ISBN: 0521285127
Size: 54.85 MB
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The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.

Probability Statistics And Analysis

Author: J. F. C. Kingman
Publisher: Cambridge University Press
ISBN: 0521285909
Size: 43.34 MB
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This collection of papers is dedicated to David Kendall, the topics will interest postgraduate and research mathematicians.

Non Autonomous Kato Classes And Feynman Kac Propagators

Author: Archil Gulisashvili
Publisher: World Scientific
ISBN: 9812774602
Size: 39.61 MB
Format: PDF, Docs
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This book aims to present the overall existing tsunami hazard in the Caribbean Sea region, a region which is typically only associated with hurricanes. It initially presents an overview of all of the existing tsunami-causing factors found in the region: earthquakes, sub-aerial and submarine landslides, and submarine explosions. This is followed by field evidence of recent and pre-historic tsunami events, which gives credibility to all of this effort. The next section is a description of the tsunami hazard mitigation efforts being carried out locally and in collaboration with national and international programs. The final part is dedicated to the presentation of related recent research results.

It S Stochastic Calculus And Probability Theory

Author: Nobuyuki Ikeda
Publisher: Springer Science & Business Media
ISBN: 4431685324
Size: 59.16 MB
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Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics. This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here. This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included.

Homogeneous Structures On Riemannian Manifolds

Author: F. Tricerri
Publisher: Cambridge University Press
ISBN: 0521274893
Size: 12.61 MB
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The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

Stochastic Analysis

Author: M. T. Barlow
Publisher: Cambridge University Press
ISBN: 0521425336
Size: 43.15 MB
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Papers from the Symposium on stochastic analysis, which took place at the University of Durham in July 1990.

Random Walks And Heat Kernels On Graphs

Author: Martin T. Barlow
Publisher: Cambridge University Press
ISBN: 1107674425
Size: 38.54 MB
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This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincar inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.