Stochastic Calculus In Manifolds

Author : Michel Emery
Publisher : Springer Science & Business Media
Page : 158 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642750519

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Stochastic Calculus in Manifolds by Michel Emery Pdf

Addressed to both pure and applied probabilitists, including graduate students, this text is a pedagogically-oriented introduction to the Schwartz-Meyer second-order geometry and its use in stochastic calculus. P.A. Meyer has contributed an appendix: "A short presentation of stochastic calculus" presenting the basis of stochastic calculus and thus making the book better accessible to non-probabilitists also. No prior knowledge of differential geometry is assumed of the reader: this is covered within the text to the extent. The general theory is presented only towards the end of the book, after the reader has been exposed to two particular instances - martingales and Brownian motions - in manifolds. The book also includes new material on non-confluence of martingales, s.d.e. from one manifold to another, approximation results for martingales, solutions to Stratonovich differential equations. Thus this book will prove very useful to specialists and non-specialists alike, as a self-contained introductory text or as a compact reference.

Author : Laurent Schwartz
Publisher : Les Presses de L'Universite de Montreal
Page : 192 pages
File Size : 52,5 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015038936186

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Semimartingales and Their Stochastic Calculus on Manifolds by Laurent Schwartz Pdf

Author : I. Iscoe
Publisher : Unknown
Page : 0 pages
File Size : 54,6 Mb
Release : 1984
Category : Electronic
ISBN : OCLC:471932056

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Semimartingales and Their Stochastic Calculus on Manifolds by I. Iscoe Pdf

Author : K. D. Elworthy,Kenneth David Elworthy
Publisher : Cambridge University Press
Page : 347 pages
File Size : 48,9 Mb
Release : 1982
Category : Manifolds (Mathematics).
ISBN : 9780521287678

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Stochastic Differential Equations on Manifolds by K. D. Elworthy,Kenneth David Elworthy Pdf

The aims of this book, originally published in 1982, are to give an understanding of the basic ideas concerning stochastic differential equations on manifolds and their solution flows, to examine the properties of Brownian motion on Riemannian manifolds when it is constructed using the stochiastic development and to indicate some of the uses of the theory. The author has included two appendices which summarise the manifold theory and differential geometry needed to follow the development; coordinate-free notation is used throughout. Moreover, the stochiastic integrals used are those which can be obtained from limits of the Riemann sums, thereby avoiding much of the technicalities of the general theory of processes and allowing the reader to get a quick grasp of the fundamental ideas of stochastic integration as they are needed for a variety of applications.

Author : Elton P. Hsu
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 50,5 Mb
Release : 2002
Category : Differential geometry
ISBN : 9780821808023

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Stochastic Analysis on Manifolds by Elton P. Hsu Pdf

Concerned with probability theory, Elton Hsu's study focuses primarily on the relations between Brownian motion on a manifold and analytical aspects of differential geometry. A key theme is the probabilistic interpretation of the curvature of a manifold

Author : Feng-Yu Wang
Publisher : World Scientific
Page : 392 pages
File Size : 44,6 Mb
Release : 2014
Category : Mathematics
ISBN : 9789814452656

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Analysis for Diffusion Processes on Riemannian Manifolds by Feng-Yu Wang Pdf

Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

Author : N. Ikeda,S. Watanabe
Publisher : Elsevier
Page : 572 pages
File Size : 51,8 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483296159

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Stochastic Differential Equations and Diffusion Processes by N. Ikeda,S. Watanabe Pdf

Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.

Author : V. Wihstutz,M.A. Pinsky
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203896

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Diffusion Processes and Related Problems in Analysis, Volume II by V. Wihstutz,M.A. Pinsky Pdf

During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.

Author : Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 48,7 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821838396

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An Introduction to the Analysis of Paths on a Riemannian Manifold by Daniel W. Stroock Pdf

Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Laurent Decreusefond,Bernt Oksendal,Ali S. Üstünel
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201571

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Stochastic Analysis and Related Topics VII by Laurent Decreusefond,Bernt Oksendal,Ali S. Üstünel Pdf

One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.

Author : Wolfgang Paul,Jörg Baschnagel
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 55,8 Mb
Release : 1999
Category : Business & Economics
ISBN : 3540665609

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Stochastic Processes by Wolfgang Paul,Jörg Baschnagel Pdf

The book is an introduction to stochastic processes with applications from physics and finance. It introduces the basic notions of probability theory and the mathematics of stochastic processes. The applications that we discuss are chosen to show the interdisciplinary character of the concepts and methods and are taken from physics and finance. Due to its interdisciplinary character and choice of topics, the book can show students and researchers in physics how models and techniques used in their field can be translated into and applied in the field of finance and risk-management. On the other hand, a practitioner from the field of finance will find models and approaches recently developed in the emerging field of econophysics for understanding the stochastic price behavior of financial assets.

Author : Pierre Del Moral,Spiridon Penev
Publisher : CRC Press
Page : 866 pages
File Size : 55,6 Mb
Release : 2017-02-24
Category : Mathematics
ISBN : 9781498701846

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Stochastic Processes by Pierre Del Moral,Spiridon Penev Pdf

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

Author : Bernt Oksendal
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 55,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662130506

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Stochastic Differential Equations by Bernt Oksendal Pdf

These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.

Author : Gregory S. Chirikjian
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 49,5 Mb
Release : 2009-09-02
Category : Mathematics
ISBN : 9780817648039

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Stochastic Models, Information Theory, and Lie Groups, Volume 1 by Gregory S. Chirikjian Pdf

This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Author : Yuri E. Gliklikh
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 47,7 Mb
Release : 2010-12-07
Category : Mathematics
ISBN : 9780857291639

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Global and Stochastic Analysis with Applications to Mathematical Physics by Yuri E. Gliklikh Pdf

Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.