Multifractals : theory and applications /: theory and applications. (©2001)

• Record Type: Book
• Further Information: Note: David Harte.
• Other Names: Harte, David
• Contents: SECTION I: INTRODUCTION AND PRELIMINARIES; MOTIVATION AND BACKGROUND; Fractal Sets and Multifractal Measures; Dynamical Systems; Turbulence; Rainfall Fields; Earthquake Modelling; Other Applications; Concept of Multifractals; Overview of Book; THE MULTIFRACTAL FORMALISM; Historical Development of Generalised Renyi Dimensions; Generlised Rényi Lattice Dimensions; Generalised Rényi Point Centred Dimensions; Multifractal Spectrum and Formalism; Review of Related Lattice Based Results; Review of Related Point Centred Results; THE MULTINOMIAL MEASURE; Local Behaviour; Global Averaging and Legendre Transforms; Fractal Dimensions; Point Centred Construction; SECTION II: MULTIFRACTAL FORMALISM USING LARGE DEVIATIONS; LATTICE BASED MULTIFRACTALS; Large Deviation Formalism; Uniform Spatial Sampling Measure; A Family of Sampling Measures; Hausdorff Dimensions; POINT CENTERED MULTIFRACTALS; Large Deviation Formalism; A Family of Sampling Measures; Hausdorff Dimensions; Relationship Between Lattice and Point Centred Constructions; MULTIPLICATIVE CASCADE PROCESSES; Moran Cascades Processes; Random Cascades; Other Cascade Processes; SECTION III: ESTIMATION OF THE RENYI DIMENSIONS; INTERPOINT DISTANCES OF ORDER q AND INTRINSIC BIAS; Boundary Effect; Multiplicity of Boundaries; Decomposition of FY(y); Differentiable Distribution; ESTIMATION OF POINT CENTRED RENYI DIMENSIONS WITH q=2; Generalised Grassberger-Procaccia Algorithm; Takens Estimator; Hill Estimator; Bootstrap Estimation Procedure; Discussion and Examples; EXTRINSIC SOURCES OF BIAS; Imposed Boundary Effect; Rounding Effect; Effect of Noise; APPLICATIONS OF DIMENSION ESTIMATION; More on Estimation and Interpretation; Spatial and Temporal Point Patterns; Dynamical Systems; Is a Process Stochastic or Deterministic?; Stochastic Processes with Powerlaw Properties; EARTHQUAKE ANALYSES; Sources of Data; Effects Causing Bias; Results; Comparison of Results and Conclusions; APPENDICES; Properties and Dimensions of Sets; Large Deviations; REFERENCES
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2001
• Copyright Date: 2001
• Extent: 1 online resource (xiii, 248 pages), illustrations
• Subjects: 514/.742; Multifractals; Fractals; Multifractals; Waarschijnlijkheidstheorie; Statistiek; Fractals; Electronic books
• Languages: English
• ISBNs: 1584881542; 9781584881544; 1420036009; 9781420036008
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.