Stochastic equations through the eye of the physicist: basic concepts, exact results and asymptotic approximations
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2005
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| Ausgabe: | 1st ed |
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| Online-Zugang: | Volltext |
| Beschreibung: | 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 Includes bibliographical references (p. 513-534) and index |
| Beschreibung: | 1 Online-Ressource (xviii, 538 p.) |
| ISBN: | 9780444517975 0444517979 9780080457642 0080457649 |
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| 500 | |a 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. | ||
| 500 | |a 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. | ||
| 500 | |a 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 | ||
| 500 | |a Includes bibliographical references (p. 513-534) and index | ||
| 650 | 4 | |a Processus stochastiques | |
| 650 | 4 | |a Analyse stochastique | |
| 650 | 4 | |a Physique mathématique | |
| 650 | 7 | |a Mathematical physics |2 fast | |
| 650 | 7 | |a Stochastic analysis |2 fast | |
| 650 | 7 | |a Stochastic processes |2 fast | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Stochastic analysis | |
| 650 | 4 | |a Mathematical physics | |
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Datensatz im Suchindex
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| author | Kli͡at͡skin, Valeriĭ Isaakovich |
| author_facet | Kli͡at͡skin, Valeriĭ Isaakovich |
| author_role | aut |
| author_sort | Kli͡at͡skin, Valeriĭ Isaakovich |
| author_variant | v i k vi vik |
| building | Verbundindex |
| bvnumber | BV042311024 |
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| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| isbn | 9780444517975 0444517979 9780080457642 0080457649 |
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| spelling | Kli͡at͡skin, Valeriĭ Isaakovich Verfasser aut Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations V.I Klyatskin 1st ed Amsterdam Elsevier 2005 1 Online-Ressource (xviii, 538 p.) txt rdacontent c rdamedia cr rdacarrier 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 Includes bibliographical references (p. 513-534) and index Processus stochastiques Analyse stochastique Physique mathématique Mathematical physics fast Stochastic analysis fast Stochastic processes fast MATHEMATICS / Probability & Statistics / General bisacsh Mathematische Physik Stochastic processes Stochastic analysis Mathematical physics http://www.sciencedirect.com/science/book/9780444517975 Verlag Volltext |
| spellingShingle | Kli͡at͡skin, Valeriĭ Isaakovich Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations Processus stochastiques Analyse stochastique Physique mathématique Mathematical physics fast Stochastic analysis fast Stochastic processes fast MATHEMATICS / Probability & Statistics / General bisacsh Mathematische Physik Stochastic processes Stochastic analysis Mathematical physics |
| title | Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations |
| title_auth | Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations |
| title_exact_search | Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations |
| title_full | Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations V.I Klyatskin |
| title_fullStr | Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations V.I Klyatskin |
| title_full_unstemmed | Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations V.I Klyatskin |
| title_short | Stochastic equations through the eye of the physicist |
| title_sort | stochastic equations through the eye of the physicist basic concepts exact results and asymptotic approximations |
| title_sub | basic concepts, exact results and asymptotic approximations |
| topic | Processus stochastiques Analyse stochastique Physique mathématique Mathematical physics fast Stochastic analysis fast Stochastic processes fast MATHEMATICS / Probability & Statistics / General bisacsh Mathematische Physik Stochastic processes Stochastic analysis Mathematical physics |
| topic_facet | Processus stochastiques Analyse stochastique Physique mathématique Mathematical physics Stochastic analysis Stochastic processes MATHEMATICS / Probability & Statistics / General Mathematische Physik |
| url | http://www.sciencedirect.com/science/book/9780444517975 |
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