Diffusion Processes And Their Sample Paths

Author : Kiyosi Itô,Henry P. Jr. McKean
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642620256

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Diffusion Processes and their Sample Paths by Kiyosi Itô,Henry P. Jr. McKean Pdf

Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.

Author : K. Ito,Henry P. McKean
Publisher : Unknown
Page : 321 pages
File Size : 48,5 Mb
Release : 1965
Category : Brownian motion processes
ISBN : 0387033025

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Diffusion Processes and Their Sample Paths by K. Ito,Henry P. McKean Pdf

Author : Kiyosi Itô,Henry P. Jr. McKean
Publisher : Springer
Page : 323 pages
File Size : 46,5 Mb
Release : 1974-01-01
Category : Mathematics
ISBN : 3540033025

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Diffusion Processes and their Sample Paths by Kiyosi Itô,Henry P. Jr. McKean Pdf

Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.

Author : Kiyosi Itō,Henry P. McKean,Henry Pratt McKean
Publisher : Unknown
Page : 352 pages
File Size : 51,5 Mb
Release : 1965
Category : Brownian motion processes
ISBN : UOM:39015015712063

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Diffusion Processes and Their Sample Paths by Kiyosi Itō,Henry P. McKean,Henry Pratt McKean Pdf

Author : Nihon Sūgakkai
Publisher : MIT Press
Page : 1180 pages
File Size : 50,9 Mb
Release : 1993
Category : Mathematics
ISBN : 0262590204

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Encyclopedic Dictionary of Mathematics by Nihon Sūgakkai Pdf

V.1. A.N. v.2. O.Z. Apendices and indexes.

Author : Daniel W. Stroock,S.R.S. Varadhan
Publisher : Springer
Page : 338 pages
File Size : 44,9 Mb
Release : 2007-02-03
Category : Mathematics
ISBN : 9783540289999

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Multidimensional Diffusion Processes by Daniel W. Stroock,S.R.S. Varadhan Pdf

From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 339 pages
File Size : 47,7 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781493913237

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Stochastic Processes and Applications by Grigorios A. Pavliotis Pdf

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Author : Fabrice Baudoin
Publisher : Erich Schmidt Verlag GmbH & Co. KG
Page : 292 pages
File Size : 51,6 Mb
Release : 2014
Category : Calculus
ISBN : 3037191333

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Diffusion Processes and Stochastic Calculus by Fabrice Baudoin Pdf

The main purpose of the book is to present, at a graduate level and in a self-contained way, the most important aspects of the theory of continuous stochastic processes in continuous time and to introduce some of its ramifications such as the theory of semigroups, the Malliavin calculus, and the Lyons' rough paths. This book is intended for students, or even researchers, who wish to learn the basics in a concise but complete and rigorous manner. Several exercises are distributed throughout the text to test the understanding of the reader and each chapter ends with bibliographic comments aimed at those interested in exploring the materials further. Stochastic calculus was developed in the 1950s and the range of its applications is huge and still growing today. Besides being a fundamental component of modern probability theory, domains of applications include but are not limited to: mathematical finance, biology, physics, and engineering sciences. The first part of the text is devoted to the general theory of stochastic processes. The author focuses on the existence and regularity results for processes and on the theory of martingales. This allows him to introduce the Brownian motion quickly and study its most fundamental properties. The second part deals with the study of Markov processes, in particular, diffusions. The author's goal is to stress the connections between these processes and the theory of evolution semigroups. The third part deals with stochastic integrals, stochastic differential equations and Malliavin calculus. In the fourth and final part, the author presents an introduction to the very new theory of rough paths by Terry Lyons.

Author : B. L. S. Prakasa Rao
Publisher : John Wiley & Sons
Page : 213 pages
File Size : 41,5 Mb
Release : 2011-07-05
Category : Mathematics
ISBN : 9780470975763

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Statistical Inference for Fractional Diffusion Processes by B. L. S. Prakasa Rao Pdf

Stochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view. This book deals with Fractional Diffusion Processes and statistical inference for such stochastic processes. The main focus of the book is to consider parametric and nonparametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable. Key features: Introduces self-similar processes, fractional Brownian motion and stochastic integration with respect to fractional Brownian motion. Provides a comprehensive review of statistical inference for processes driven by fractional Brownian motion for modelling long range dependence. Presents a study of parametric and nonparametric inference problems for the fractional diffusion process. Discusses the fractional Brownian sheet and infinite dimensional fractional Brownian motion. Includes recent results and developments in the area of statistical inference of fractional diffusion processes. Researchers and students working on the statistics of fractional diffusion processes and applied mathematicians and statisticians involved in stochastic process modelling will benefit from this book.

Author : Kazuaki Taira
Publisher : Springer Nature
Page : 792 pages
File Size : 52,6 Mb
Release : 2022-05-28
Category : Mathematics
ISBN : 9789811910999

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Functional Analytic Techniques for Diffusion Processes by Kazuaki Taira Pdf

This book is an easy-to-read reference providing a link between functional analysis and diffusion processes. More precisely, the book takes readers to a mathematical crossroads of functional analysis (macroscopic approach), partial differential equations (mesoscopic approach), and probability (microscopic approach) via the mathematics needed for the hard parts of diffusion processes. This work brings these three fields of analysis together and provides a profound stochastic insight (microscopic approach) into the study of elliptic boundary value problems. The author does a massive study of diffusion processes from a broad perspective and explains mathematical matters in a more easily readable way than one usually would find. The book is amply illustrated; 14 tables and 141 figures are provided with appropriate captions in such a fashion that readers can easily understand powerful techniques of functional analysis for the study of diffusion processes in probability. The scope of the author’s work has been and continues to be powerful methods of functional analysis for future research of elliptic boundary value problems and Markov processes via semigroups. A broad spectrum of readers can appreciate easily and effectively the stochastic intuition that this book conveys. Furthermore, the book will serve as a sound basis both for researchers and for graduate students in pure and applied mathematics who are interested in a modern version of the classical potential theory and Markov processes. For advanced undergraduates working in functional analysis, partial differential equations, and probability, it provides an effective opening to these three interrelated fields of analysis. Beginning graduate students and mathematicians in the field looking for a coherent overview will find the book to be a helpful beginning. This work will be a major influence in a very broad field of study for a long time.

Author : Shiing-Shen Chern,Friedrich Hirzebruch
Publisher : World Scientific
Page : 780 pages
File Size : 47,7 Mb
Release : 2000
Category : Mathematics
ISBN : 9810239459

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Wolf Prize in Mathematics by Shiing-Shen Chern,Friedrich Hirzebruch Pdf

This invaluable book features bibliographies, important papers, and speeches (for example at international congresses) of Wolf Prize winners. This is the first time that lectures by some Wolf Prize winners have been published together. Since the work of the Wolf laureates covers a wide spectrum, much of the mathematics of the twentieth century comes to life in this book.

Author : J. Hoffman-Jorgensen
Publisher : Routledge
Page : 296 pages
File Size : 40,5 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351421546

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Probability With a View Towards Statistics, Volume II by J. Hoffman-Jorgensen Pdf

Volume II of this two-volume text and reference work concentrates on the applications of probability theory to statistics, e.g., the art of calculating densities of complicated transformations of random vectors, exponential models, consistency of maximum estimators, and asymptotic normality of maximum estimators. It also discusses topics of a pure probabilistic nature, such as stochastic processes, regular conditional probabilities, strong Markov chains, random walks, and optimal stopping strategies in random games. Unusual topics include the transformation theory of densities using Hausdorff measures, the consistency theory using the upper definition function, and the asymptotic normality of maximum estimators using twice stochastic differentiability. With an emphasis on applications to statistics, this is a continuation of the first volume, though it may be used independently of that book. Assuming a knowledge of linear algebra and analysis, as well as a course in modern probability, Volume II looks at statistics from a probabilistic point of view, touching only slightly on the practical computation aspects.

Author : Lajos Horvath and Barbara Szyszkowicz
Publisher : American Mathematical Soc.
Page : 552 pages
File Size : 41,6 Mb
Release : 2024-06-07
Category : Asymptotic expansions
ISBN : 082187148X

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Asymptotic Methods in Stochastics by Lajos Horvath and Barbara Szyszkowicz Pdf

Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.

Author : F. Alberto Grünbaum,Pierre van Moerbeke,Victor H. Moll
Publisher : Birkhäuser
Page : 418 pages
File Size : 46,9 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 9783319222370

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Henry P. McKean Jr. Selecta by F. Alberto Grünbaum,Pierre van Moerbeke,Victor H. Moll Pdf

This volume presents a selection of papers by Henry P. McKean, which illustrate the various areas in mathematics in which he has made seminal contributions. Topics covered include probability theory, integrable systems, geometry and financial mathematics. Each paper represents a contribution by Prof. McKean, either alone or together with other researchers, that has had a profound influence in the respective area.

Author : Samuel Karlin,Howard M. Taylor
Publisher : Gulf Professional Publishing
Page : 568 pages
File Size : 48,9 Mb
Release : 1981-05-12
Category : Business & Economics
ISBN : 0123986508

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A Second Course in Stochastic Processes by Samuel Karlin,Howard M. Taylor Pdf

Algebraic methods in markov chains; Ratio theorems of transition probabilities and applications; Sums of independent random variables as a markov chain; Order statistics, poisson processes, and applications; Continuous time markov chains; Diffusion processes; Compouding stochastic processes; Fluctuation theory of partial sums of independent identically distributed random variables; Queueing processes.