Kooperativer Bibliotheksverbund

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Format: XXI, 323 S. : , Ill.

Edition: 1st publ.

Series Statement: Cambridge nonlinear science series 2

Subjects: Physics

Keywords: Chaos ; Dynamisches System ; Algorithmus ; Fraktal ; Chaostheorie

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: http://www.loc.gov/catdir/toc/cam041/93120880.html

URL: http://www.loc.gov/catdir/description/cam041/93120880.html

UID:

Format: XVII, 469 S. : , graph. Darst.

Edition: 1. publ.

ISBN: 0-521-48132-5 , 0-521-57882-5

Language: English

Subjects: Physics

Keywords: Mechanik

URL: Inhaltstext

UID:

Format: 1 online resource (xi, 206 pages) : , digital, PDF file(s).

Edition: 1st ed.

ISBN: 1-107-23323-2 , 1-107-33291-5 , 1-107-33457-8 , 1-107-33623-6 , 1-139-01946-5 , 1-299-25742-9 , 1-107-33226-5 , 1-107-33540-X

Content: Stochastic calculus provides a powerful description of a specific class of stochastic processes in physics and finance. However, many econophysicists struggle to understand it. This book presents the subject simply and systematically, giving graduate students and practitioners a better understanding and enabling them to apply the methods in practice. The book develops Ito calculus and Fokker-Planck equations as parallel approaches to stochastic processes, using those methods in a unified way. The focus is on nonstationary processes, and statistical ensembles are emphasized in time series analysis. Stochastic calculus is developed using general martingales. Scaling and fat tails are presented via diffusive models. Fractional Brownian motion is thoroughly analyzed and contrasted with Ito processes. The Chapman-Kolmogorov and Fokker-Planck equations are shown in theory and by example to be more general than a Markov process. The book also presents new ideas in financial economics and a critical survey of econometrics.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Random variables and probability distributions -- Martingales, Markov, and nonstationarity -- Stochastic calculus -- Ito processes and Fokker-Planck equations -- Selfsimilar Ito processes -- Fractional Brownian motion -- Kolmogorov's PDEs and Chapman-Kolmogorov -- Non Markov Ito processes -- Black-Scholes, martingales, and Feynman-Katz -- Stochastic calculus with martingales -- Statistical physics and finance, a brief history of each -- Introduction to new financial economics -- Statistical ensembles and time series analysis -- Econometrics -- Semimartingales. , English

Additional Edition: ISBN 0-521-76340-1

Additional Edition: ISBN 1-107-32647-8

Language: English

URL: Volltext  (lizenzpflichtig)

URL: Inhaltstext

URL: https://doi.org/10.1017/CBO9781139019460

URL: https://doi.org/10.1017/CBO9781139019460

UID:

Format: 1 online resource (xvi, 209 pages) : , digital, PDF file(s).

ISBN: 0-511-83863-8 , 0-511-60658-3

Content: Standard texts and research in economics and finance ignore the absence of evidence from the analysis of real, unmassaged market data to support the notion of Adam Smith's stabilizing Invisible Hand. The neo-classical equilibrium model forms the theoretical basis for the positions of the US Treasury, the World Bank and the European Union, accepting it as their credo. It provides the theoretical underpinning for globalization, expecting to achieve the best of all possible worlds via the deregulation of all markets. In stark contrast, this text introduces a empirically based model of financial market dynamics that explains volatility, prices options correctly and clarifies the instability of financial markets. The emphasis is on understanding how real markets behave, not how they hypothetically 'should' behave. This text is written for physics graduate students and finance specialists, but will also serve as a valuable resource for those with a less mathematical background.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , English

Additional Edition: ISBN 0-521-03628-3

Additional Edition: ISBN 0-521-82447-8

Language: English

Subjects: Economics , Mathematics

URL: Volltext  (lizenzpflichtig)

URL: Inhaltstext

URL: https://doi.org/10.1017/CBO9780511606588

URL: https://doi.org/10.1017/CBO9780511606588

UID:

Format: 56 S.

ISBN: 91-87308-28-2

Series Statement: Physica scripta / T 20

Keywords: Nichtlineare Dynamik ; Chaostheorie ; Nichtlineares dynamisches System ; Chaos ; Einführung ; Einführung ; Einführung

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Format: 1 online resource (xv, 270 pages) : , digital, PDF file(s).

Edition: Second edition.

ISBN: 9780511805448 (ebook)

Content: This second edition presents the advances made in finance market analysis since 2005. The book provides a careful introduction to stochastic methods along with approximate ensembles for a single, historic time series. The new edition explains the history leading up to the biggest economic disaster of the 21st century. Empirical evidence for finance market instability under deregulation is given, together with a history of the explosion of the US Dollar worldwide. A model shows how bounds set by a central bank stabilized FX in the gold standard era, illustrating the effect of regulations. The book presents economic and finance theory thoroughly and critically, including rational expectations, cointegration and arch/garch methods, and replaces several of those misconceptions by empirically based ideas. This book will be of interest to finance theorists, traders, economists, physicists and engineers, and leads the reader to the frontier of research in time series analysis.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Econophysics : why and what -- Neo-classical economic theory -- Probability and stochastic processes -- Introduction to financial economics -- Introduction to portfolio selection theory -- Scaling, pair correlations, and conditional densities -- Statistical ensembles : deducing dynamics from time series -- Martingale option pricing -- FX market globalization : evolution of the dollar to worldwide reserve currency -- Macroeconomics and econometrics : regression models vs empirically based modeling -- Complexity.

Additional Edition: Print version: ISBN 9780521429627

Language: English

Subjects: Economics , Mathematics

URL: https://doi.org/10.1017/CBO9780511805448

URL: Volltext  (lizenzpflichtig)

URL: Inhaltstext

URL: https://doi.org/10.1017/CBO9780511805448

UID:

Format: 1 online resource (xvii, 469 pages) : , digital, PDF file(s).

ISBN: 1-139-17093-7

Content: This is an advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It was the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organising principle of the text is integrability vs. nonintegrability. Flows in phase space and transformations are introduced early and systematically and are applied throughout the text. The standard integrable problems of elementary physics are analysed from the standpoint of flows, transformations, and integrability. This approach then allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will be of value to physicists and engineers taking graduate courses in classical mechanics. It will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Cover -- Frontmatter -- Contents -- Foreword -- Acknowledgements -- Universal laws of nature -- 1.1 Mechanics in the context of history -- 1.2 The foundations of mechanics -- 1.3 Conservation laws for N bodies -- 1.4 The geometric invariance principles of physics -- 1.5 Co variance of vector equations vs invariance of solutions -- Exercises -- Lagrange's and Hamilton's equations -- 2.1 Overview -- 2.2 Extrema of functional -- 2.3 Newton's equations from the action principle -- 2.4 Arbitrary coordinate transformations and Lagrange's equations -- 2.5 Constrained Lagrangian systems -- 2.6 Symmetry, invariance, and conservation laws -- 2.7 Gauge invariance -- 2.8 Hamilton's canonical equations -- Exercises -- Flows in phase space -- 3.1 Solvable vs integrable -- 3.2 Streamline motions and Liouville's theorem -- 3.3 Equilibria and linear stability theory -- 3.4 One degree of freedom Hamiltonian systems -- 3.5 Introduction to 'clockwork': stable periodic and stable quasiperiodic orbits -- 3.6 Introduction to integrable flows -- 3.7 Bifurcations in Hamiltonian systems -- Exercises -- Motion in a central potential -- 4.1 Overview -- 4.2 Integration via two constants of the motion -- 4.3 Maps, winding numbers, and orbital stability -- 4.4 Clockwork is rare in mechanical systems -- 4.5 Hidden symmetry in the Kepler problem -- 4.6 Periodicity and nonperiodicity that are not like clockwork -- Exercises -- Small oscillations about equilibria -- 5.1 Introduction -- 5.2 The normal mode transformation -- 5.3 Coupled pendulums -- Exercises -- Integrable and chaotic oscillations -- 6.1 Qualitative theory of integrable canonical systems -- 6.2 Return maps -- 6.3 A chaotic nonintegrable system -- 6.4 Area-preserving maps -- 6.5 Computation of exact chaotic orbits -- 6.6 On the nature of deterministic chaos -- Exercises -- Parameter-dependent transformations. , 7.1 Introduction -- 7.2 Phase flows as transformation groups -- 7.3 One-parameter groups of transformations -- 7.4 Two definitions of integrability -- 7.5 Invariance under transformations of coordinates -- 7.6 Power series solutions of systems of differential equations -- 7.7 Lie algebras of vector fields -- Exercises -- Linear transformations, rotations, and rotating frames -- 8.1 Overview -- 8.2 Similarity transformations -- 8.3 Linear transformations and eigenvalue problems -- 8.4 Rotations form a Lie group -- 8.5 Dynamics in rotating reference frames -- Exercises -- Rigid body motions -- 9.1 Euler's equations of rigid body motion -- 9.2 Euler's rigid body -- 9.3 The Euler angles -- 9.4 Lagrange's top -- 9.5 Integrable problems in rigid body dynamics -- 9.6 Noncanonical flows as iterated maps -- 9.7 Nonintegrable rigid body motions -- Exercises -- Lagrangian dynamics and transformations in configuration space -- 10.1 Invariance and covariance -- 10.2 Geometry of the motion in configuration space -- 10.3 Basis vectors in configuration space -- 10.4 Canonical momenta and covariance of Lagrange's equations in configuration space -- Exercises -- Relativity, geometry, and gravity -- 11.1 Electrodynamics -- 11.2 The principle of relativity -- 11.3 Coordinate systems and integrability on manifolds -- 11.4 Force-free motion on curved manifolds -- 11.5 Newtonian gravity as geometry in curved space-time -- 11.6 Einstein's gravitational field equations -- 11.7 In variance principles and laws of nature -- Exercises -- Generalized vs nonholonomic coordinates -- 12.1 Group parameters as nonholonomic coordinates -- 12.2 Euler-Lagrange equations for nonintegrable velocities -- 12.3 Group parameters as generalized coordinates -- Exercises -- Noncanonical flows -- 13.1 Flows on spheres -- 13.2 Local vs complete integrability. , 13.3 Globally integrable noncanonical flows -- 13.4 Attractors -- 13.5 Damped-driven Euler-Lagrange dynamics -- 13.6 Liapunov exponents, geometry, and integrability -- Exercises -- Damped-driven Newtonian systems -- 14.1 Period doubling in physics -- 14.2 Fractal and multifractal orbits in phase space -- 14.3 Strange attractors -- 14.4 The two-frequency problem -- Exercises -- Hamiltonian dynamics and transformations in phase space -- 15.1 Generating functions for canonical transformations -- 15.2 Poisson brackets and infinitesimal transformations: symmetry, invariance, and conservation laws -- 15.3 Lie algebras of Hamiltonian flows -- 15.4 The Dirac quantization rules -- 15.5 Hidden symmetry: superintegrability of the Kepler and isotropic harmonic oscillator problems -- 15.6 Noncanonical Hamiltonian flows -- Exercises -- Integrable canonical flows -- 16.1 Solution by canonical transformations -- 16.2 The Hamilton-Jacobi equation -- 16.3 Integrability and symmetry -- 16.4 Action-angle variables -- 16.5 Central potentials -- 16.6 The action integral in quantum theory -- Exercises -- Nonintegrable canonical flows -- 17.1 The Henón-Heiles model -- 17.2 Perturbation theory and averaging -- 17.3 The standard map -- 17.4 The Kolmogorov-Arnol'd-Moser (KAM) theorem -- 17.5 Is clockwork possible in the solar system? -- Exercises -- Simulations, complexity, and laws of nature -- 18.1 Integrability, chaos, and complexity -- 18.2 Simulations and modelling without invariance -- 18.3 History in the context of mechanics -- Exercises -- Bibliography -- Index. , English

Additional Edition: ISBN 0-521-57882-5

Additional Edition: ISBN 0-521-48132-5

Language: English

URL: Volltext  (lizenzpflichtig)

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: https://doi.org/10.1017/CBO9781139170932

UID:

Format: XVI, 209 S. : Ill., graph. Darst.

ISBN: 0-521-82447-8

Note: Includes bibliographical references (p. 201-206) and index

Language: English

Subjects: Economics

Keywords: Kreditmarkt ; Mathematisches Modell ; Finanzmathematik

URL: Publisher description

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012769137&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: http://www.loc.gov/catdir/description/cam041/2003060538.html

URL: http://www.loc.gov/catdir/description/cam051/2003060538.html

URL: http://www.loc.gov/catdir/enhancements/fy0732/2003060538-b.html

UID:

Format: 1 online resource (xxi, 323 pages) : , digital, PDF file(s).

ISBN: 1-107-38371-4 , 1-107-38492-3 , 1-107-39857-6 , 1-107-39015-X , 1-107-38730-2 , 0-511-56415-5

Series Statement: Cambridge nonlinear science series ; 2

Content: This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Cover; Half Title; Title Page; Copyright; Dedication; Contents; Preface; Introduction; 1 Flows in phase space; 1.1 Determinism, phase flows, and Liouville's theorem; 1.2 Equilibria, linear stability, and limit cycles; 1.3 Change of stability (bifurcations); 1.4 Periodically driven systems and stroboscopic maps; 1.5 Continuous groups of transformations as phase space flows; 2 Introduction to deterministic chaos; 2.1 The Lorenz model, the Lorenz plot, and the binary tent map; 2.2 Local exponential instability of nearby orbits: the positiveLiapunov exponent , 2.3 The Frobenius-Peron equation (invariant densities)2.4 Simple examples of fully developed chaos for maps of theinterval; 2.5 Maps that are conjugate under differentiable coordinatetransformations; 2.6 Computation of nonperiodic chaotic orbits at fullydeveloped chaos; 2.7 Is the idea of randomness necessary in natural science?; 3 Conservative dynamical systems; 3.1 Integrable conservative systems: symmetry, invariance, conservation laws, and motion on invariant tori in phase space; 3.2 The Hénon-Heiles model: evidence for bifurcations from integrable to chaotic behavior , 3.3 Perturbed twist maps: nearly integrable conservativesystems3.4 Mixing and ergodicity: the approach to statisticalequilibrium; 3.5 The bakers' transformation; 3.6 Computation of chaotic orbits for an area-preserving map; Appendix 3.A Generating functions for canonicaltransformations; Appendix 3.B Systems in involution; 4 Fractals and fragmentation in phase space; 4.1 Introduction to fractals; 4.2 Geometrically selfsimilar fractals; 4.3 The dissipative bakers' transformation: a model 'strange' attractor; 4.4 The symmetric tent map: a model 'strange' repeller , 4.5 The devil's staircase: arithmetic on the Cantor set4.6 Generalized dimensions and the coarsegraining of phasespace; 4.7 Computation of chaotic orbits on a fractal; 5 The way to chaos by instability of quasiperiodic orbits; 5.1 From limit cycles to tori to chaos; 5.2 Periodically driven systems and circle maps; 5.3 Arnol'd tongues and the devil's staircase; 5.4 Scaling laws and renormalization group equations; 5.5 The Farey tree; 6 The way to chaos by period doubling; 6.1 Universality at transitions to chaos; 6.2 Instability of periodic orbits by period doubling , 6.3 Universal scaling for noninvertible quadratic maps of theinterval7 Introduction tomultifractals; 7.1 Incomplete but optimal information: the natural coarsegraining of phase space; 7.2 The f(α)-spectrum; 7.3 The asymmetric tent map and the two-scale Cantor set (f(α) and entropy); 7.4 Multifractals at the borderlines of chaos; 8 Statistical mechanics on symbol sequences; 8.1 Introduction to statistical mechanics; 8.2 Introduction to symbolic dynamics; 8.3 The transfer matrix method; 8.4 What is the temperature of chaotic motion on a fractal? , English

Additional Edition: ISBN 0-521-46747-0

Additional Edition: ISBN 0-521-41658-2

Language: English

URL: Volltext

URL: Inhaltstext

URL: https://doi.org/10.1017/CBO9780511564154

UID:

Format: XV, 270 S. : , graph. Darst.

Edition: 2. ed.

ISBN: 978-0-521-42962-7

Note: Incl. bibliogr. references [S. 261 - 267]

Language: English

Subjects: Economics , Mathematics

Keywords: Kreditmarkt ; Mathematisches Modell ; Finanzmathematik

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018718614&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis