L Vy Processes In Lie Groups
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Invariant Markov Processes Under Lie Group Actions
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Author : Ming Liao
language : en
Publisher: Springer
Release Date : 2018-06-28
Invariant Markov Processes Under Lie Group Actions written by Ming Liao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-28 with Mathematics categories.
The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Lévy-Khinchin representation. It interweaves probability theory, topology, and global analysis on manifolds to present the most recent results in a developing area of stochastic analysis. The author’s discussion is structured with three different levels of generality:— A Markov process in a Lie group G that is invariant under the left (or right) translations— A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X— A Markov process xt invariant under the non-transitive action of a Lie group GA large portion of the text is devoted to the representation of inhomogeneous Lévy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property. Preliminary definitions and results in both stochastics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas. Invariant Markov Processes Under Lie Group Actions will be of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.
Lie Groups And Algebraic Groups
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Author : Arkadij L. Onishchik
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lie Groups And Algebraic Groups written by Arkadij L. Onishchik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.
Group Theoretical Methods In Physics
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Author : M. A. Markov
language : en
Publisher: CRC Press
Release Date : 1985
Group Theoretical Methods In Physics written by M. A. Markov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Science categories.
Methods For Constructing Exact Solutions Of Partial Differential Equations
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Author : Sergey V. Meleshko
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-18
Methods For Constructing Exact Solutions Of Partial Differential Equations written by Sergey V. Meleshko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-18 with Technology & Engineering categories.
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Lie Group Machine Learning
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Author : Fanzhang Li
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05
Lie Group Machine Learning written by Fanzhang Li and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Computers categories.
This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.
Group Theoretic Methods In Bifurcation Theory
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Author : David H. Sattinger
language : en
Publisher: Springer
Release Date : 2006-11-15
Group Theoretic Methods In Bifurcation Theory written by David H. Sattinger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Ischemia and Loss of Vascular Autoregulation in Ocular and Cerebral Diseases: A New Perspective presents evidence that ischemia and loss of autoregulation of blood flow are associated with the onset of the major ocular and cerebral diseases including macular degeneration, diabetic retinopathy, low and normal tension open angle glaucoma, stroke and Alzheimer's disease. Recognition of these vascular changes underline the critical need for clinicians to monitor blood flow and autoregulation to improve early diagnosis and to optimize therapies of ocular and cerebral vascular diseases. The text brings to clinicians in Ophthalmology, Neurology, Medicine, Optometry and Geriatrics decisive guidance on the practical aspects for early diagnosis and treatment of ocular and cerebral diseases. The author brings together in a concise form the progress made over the span of his career and provides new perspectives and understanding of the fluid circulations of the eye and the brain. In addition, he explains the new analytical technologies that made the new concepts possible. The physiological and functional importance of blood flow autoregulation in the eye and in the brain in minimizing the progression of pathology, including the ischemia resulting from stenosis of the internal carotid artery and stroke, are also presented . ABOUT THE AUTHOR: Dr. Langham was born in London, England. In 1947, he joined the Ophthalmological Research Unit, newly formed by the Medical Research Council of the United Kingdom under the direction of Sir Stewart Duke-Elder. In 1956, the author enjoyed a research fellowship at Harvard University. After returning to England for a time, he accepted a position of Associate Professor of Ophthalmology and Director of Research at the Wilmer Ophthalmological Institute of the Johns Hopkins Hospital and Medical school in 1959. There he initiated a program in which all residents spent time engaged in research. This productive interaction between the disciplines led to many important clinical diagnostic and therapeutic advances.
Real And Stochastic Analysis
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Author : M. M. Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Real And Stochastic Analysis written by M. M. Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.
Lie Methods In Deformation Theory
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Author : Marco Manetti
language : en
Publisher: Springer Nature
Release Date : 2022-08-01
Lie Methods In Deformation Theory written by Marco Manetti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-01 with Mathematics categories.
This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.
L Vy Processes And Stochastic Calculus
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Author : David Applebaum
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-30
L Vy Processes And Stochastic Calculus written by David Applebaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-30 with Mathematics categories.
Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Geometric Methods In System Theory
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Author : D.Q. Mayne
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Methods In System Theory written by D.Q. Mayne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.