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Author: Yuri E. Gliklikh
Publisher: Springer Science & Business Media
ISBN: 0857291637
Category : Mathematics
Languages : en
Pages : 454
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Book Description
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.
Author: Yuri E. Gliklikh
Publisher: Springer Science & Business Media
ISBN: 0857291637
Category : Mathematics
Languages : en
Pages : 454
Get Book
Book Description
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.
Author: A.B. Cruzeiro
Publisher: Springer Science & Business Media
ISBN: 1461201276
Category : Mathematics
Languages : en
Pages : 162
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Book Description
This volume represents the outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. It is a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics. Key topics covered include: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, and many others.
Author: Sergio Albeverio
Publisher: Courier Dover Publications
ISBN: 0486468992
Category : Mathematics
Languages : en
Pages : 529
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Book Description
Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.
Author: Grigori N. Milstein
Publisher: Springer Nature
ISBN: 3030820408
Category : Computers
Languages : en
Pages : 754
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Book Description
This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
Author: Kurt Jacobs
Publisher: Cambridge University Press
ISBN: 1139486799
Category : Science
Languages : en
Pages : 203
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Book Description
Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.
Author: Rolando Rebolledo
Publisher: Springer Science & Business Media
ISBN: 146121372X
Category : Mathematics
Languages : en
Pages : 168
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Book Description
The seminar on Stochastic Analysis and Mathematical Physics started in 1984 at the Catholic University of Chile in Santiago and has been an on going research activity. Since 1995, the group has organized international workshops as a way of promoting a broader dialogue among experts in the areas of classical and quantum stochastic analysis, mathematical physics and physics. This volume, consisting primarily of contributions to the Third Inter national Workshop on Stochastic Analysis and Mathematical Physics (in Spanish ANESTOC), held in Santiago, Chile, in October 1998, focuses on an analysis of quantum dynamics and related problems in probability the ory. Various articles investigate quantum dynamical semigroups and new results on q-deformed oscillator algebras, while others examine the appli cation of classical stochastic processes in quantum modeling. As in previous workshops, the topic of quantum flows and semigroups occupied an important place. In her paper, R. Carbone uses a spectral type analysis to obtain exponential rates of convergence towards the equilibrium of a quantum dynamical semigroup in the £2 sense. The method is illus trated with a quantum extension of a classical birth and death process. Quantum extensions of classical Markov processes lead to subtle problems of domains. This is in particular illustrated by F. Fagnola, who presents a pathological example of a semigroup for which the largest * -subalgebra (of the von Neumann algebra of bounded linear operators of £2 (lR+, IC)), con tained in the domain of its infinitesimal generator, is not a-weakly dense.
Author: M. M. Rao
Publisher: Courier Corporation
ISBN: 0486296539
Category : Mathematics
Languages : en
Pages : 320
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Book Description
This volume considers fundamental theories and contrasts the natural interplay between real and abstract methods. No prior knowledge of probability is assumed. Numerous problems, most with hints. 1981 edition.
Author: Zhi-yuan Huang
Publisher: Springer Science & Business Media
ISBN: 9401141088
Category : Mathematics
Languages : en
Pages : 308
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Book Description
The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).
Author: Rolando Rebolledo
Publisher: Birkhäuser
ISBN: 3034880189
Category : Mathematics
Languages : en
Pages : 172
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Book Description
The seminar on Stochastic Analysis and Mathematical Physics of the Ca tholic University of Chile, started in Santiago in 1984, has being followed and enlarged since 1995 by a series of international workshops aimed at pro moting a wide-spectrum dialogue between experts on the fields of classical and quantum stochastic analysis, mathematical physics, and physics. This volume collects most of the contributions to the Fourth Interna tional Workshop on Stochastic Analysis and Mathematical Physics (whose Spanish abbreviation is "ANESTOC"; in English, "STAMP"), held in San tiago, Chile, from January 5 to 11, 2000. The workshop style stimulated a vivid exchange of ideas which finally led to a number of written con tributions which I am glad to introduce here. However, we are currently submitted to a sort of invasion of proceedings books, and we do not want to increase our own shelves with a new one of the like. On the other hand, the editors of conference proceedings have to use different exhausting and com pulsive strategies to persuade authors to write and provide texts in time, a task which terrifies us. As a result, this volume is aimed at smoothly start ing a new kind of publication. What we would like to have is a collection of books organized like our seminar.
Author: Zeev Schuss
Publisher: Springer Science & Business Media
ISBN: 1441916059
Category : Mathematics
Languages : en
Pages : 486
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Book Description
Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.
