Stochastic Equations Through The Eye Of The Physicist

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Stochastic Equations Through The Eye Of The Physicist

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Author : Valery I. Klyatskin
language : en
Publisher: Elsevier
Release Date : 2005-05-20

Stochastic Equations Through The Eye Of The Physicist written by Valery I. Klyatskin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-20 with Science categories.

Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''oil slicks''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere. Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields. The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data. This raises a host of challenging mathematical issues. One could rarely solve such systems exactly (or approximately) in a closed analytic form, and their solutions depend in a complicated implicit manner on the initial-boundary data, forcing and system's (media) parameters . In mathematical terms such solution becomes a complicated "nonlinear functional" of random fields and processes. Part I gives mathematical formulation for the basic physical models of transport, diffusion, propagation and develops some analytic tools. Part II and III sets up and applies the techniques of variational calculus and stochastic analysis, like Fokker-Plank equation to those models, to produce exact or approximate solutions, or in worst case numeric procedures. The exposition is motivated and demonstrated with numerous examples. Part IV takes up issues for the coherent phenomena in stochastic dynamical systems, described by ordinary and partial differential equations, like wave propagation in randomly layered media (localization), turbulent advection of passive tracers (clustering), wave propagation in disordered 2D and 3D media. For the sake of reader I provide several appendixes (Part V) that give many technical mathematical details needed in the book. For scientists dealing with stochastic dynamic systems in different areas, such as hydrodynamics, acoustics, radio wave physics, theoretical and mathematical physics, and applied mathematics The theory of stochastic in terms of the functional analysis Referencing those papers, which are used or discussed in this book and also recent review papers with extensive bibliography on the subject

Stochastic Equations Theory And Applications In Acoustics Hydrodynamics Magnetohydrodynamics And Radiophysics Volume 1

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Author : Valery I. Klyatskin
language : en
Publisher: Springer
Release Date : 2014-07-14

Stochastic Equations Theory And Applications In Acoustics Hydrodynamics Magnetohydrodynamics And Radiophysics Volume 1 written by Valery I. Klyatskin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Technology & Engineering categories.

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.

Stochastic Equations Of Mathematical Physics

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Author : Jürgen vom Scheidt
language : de
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1991-01-14

Stochastic Equations Of Mathematical Physics written by Jürgen vom Scheidt 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 1991-01-14 with Mathematics categories.

Keine ausführliche Beschreibung für "Stochastic Equations of Mathematical Physics" verfügbar.

Stochastic Equations Theory And Applications In Acoustics Hydrodynamics Magnetohydrodynamics And Radiophysics Volume 2

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Author : Valery I. Klyatskin
language : en
Publisher: Springer
Release Date : 2014-07-14

Stochastic Equations Theory And Applications In Acoustics Hydrodynamics Magnetohydrodynamics And Radiophysics Volume 2 written by Valery I. Klyatskin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Technology & Engineering categories.

In some cases, certain coherent structures can exist in stochastic dynamic systems almost in every particular realization of random parameters describing these systems. Dynamic localization in one-dimensional dynamic systems, vortexgenesis (vortex production) in hydrodynamic flows, and phenomenon of clustering of various fields in random media (i.e., appearance of small regions with enhanced content of the field against the nearly vanishing background of this field in the remaining portion of space) are examples of such structure formation. The general methodology presented in Volume 1 is used in Volume 2 Coherent Phenomena in Stochastic Dynamic Systems to expound the theory of these phenomena in some specific fields of stochastic science, among which are hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics. The material of this volume includes particle and field clustering in the cases of scalar (density field) and vector (magnetic field) passive tracers in a random velocity field, dynamic localization of plane waves in layered random media, as well as monochromatic wave propagation and caustic structure formation in random media in terms of the scalar parabolic equation.

Stochastic Numerics For Mathematical Physics

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Author : Grigori N. Milstein
language : en
Publisher: Springer Nature
Release Date : 2021-12-03

Stochastic Numerics For Mathematical Physics written by Grigori N. Milstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-03 with Computers categories.

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.

Global And Stochastic Analysis With Applications To Mathematical Physics

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Author : Yuri E. Gliklikh
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-07

Global And Stochastic Analysis With Applications To Mathematical Physics written by Yuri E. Gliklikh 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 2010-12-07 with Mathematics categories.

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.

Stochastic Processes In Mathematical Physics And Engineering

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Author : Richard Ernest Bellman
language : en
Publisher: American Mathematical Soc.
Release Date : 1964-12-31

Stochastic Processes In Mathematical Physics And Engineering written by Richard Ernest Bellman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964-12-31 with Stochastic processes categories.

Stochastic Analysis And Mathematical Physics

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Author : A.B. Cruzeiro
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stochastic Analysis And Mathematical Physics written by A.B. Cruzeiro 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 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.

Nonstandard Methods In Stochastic Analysis And Mathematical Physics

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Author : Sergio Albeverio
language : en
Publisher: Courier Dover Publications
Release Date : 2009-02-26

Nonstandard Methods In Stochastic Analysis And Mathematical Physics written by Sergio Albeverio and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-26 with Mathematics categories.

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.

Stochastic Analysis And Applications In Physics

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Author : Ana Isabel Cardoso
language : en
Publisher: Springer Science & Business Media
Release Date : 1994

Stochastic Analysis And Applications In Physics written by Ana Isabel Cardoso 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 1994 with Mathematics categories.

The intensive exchange between mathematicians and users has led in recent years to a rapid development of stochastic analysis. Of the users, the physicists form perhaps the most important group, giving direction to the mathematicians' research and providing a source of intuition. White noise analysis has emerged as a viable framework for stochastic and infinite dimensional analysis. Another growth area is the theory of stochastic partial differential equations. Gauge field theories are attracting increasing attention. Dirichlet forms provide a fruitful link between the mathematics of Markov processes and the physics of quantum systems. The deterministic-stochastic interface is addressed, as are Euclidean quantum mechanics, excursions of diffusions and the convergence of Markov chains to thermal states.