Chance and Stability : Stable Distributions and their Applications
Vladimir V. Uchaikin
Bok Engelsk 2011 · Electronic books.
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| Utgitt | Munchen : : De Gruyter, , 2011.
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| Omfang | 1 online resource (598 p.)
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| Opplysninger | Description based upon print version of record.. - ""Contents""; ""Foreword""; ""Introduction""; ""I Theory""; ""1 Probability""; ""1.1 Probability space""; ""1.2 Random variables""; ""1.3 Functions Π(λ)""; ""1.4 Random vectors and processes""; ""1.5 Independence""; ""1.6 Mean and variance""; ""1.7 Bernoulli theorem""; ""1.8 The Moivre-Laplace theorem""; ""1.9 The law of large numbers""; ""1.10 Strong law of large numbers""; ""1.11 Ergodicity and stationarity""; ""1.12 The central limit theorem""; ""2 Elementary introduction to the theory of stable laws""; ""2.1 Convolutions of distributions"". - ""2.2 The Gauss distribution and the stability property""""2.3 The Cauchy and Lévy distributions""; ""2.4 Summation of strictly stable random variables""; ""2.5 The stable laws as limiting distributions""; ""2.6 Summary""; ""3 Characteristic functions""; ""3.1 Characteristic functions""; ""3.2 The characteristic functions of symmetric stable distributions""; ""3.3 Skew stable distributions with α < 1""; ""3.4 The general form of stable characteristic functions""; ""3.5 Stable laws as infinitely divisible laws""; ""3.6 Various forms of stable characteristic functions"". - ""3.7 Some properties of stable random variables""""3.8 Conclusion""; ""4 Probability densities""; ""4.1 Symmetric distributions""; ""4.2 Convergent series for asymmetric distributions""; ""4.3 Long tails""; ""4.4 Integral representation of stable densities""; ""4.5 Integral representation of stable distribution functions""; ""4.6 Duality law""; ""4.7 Short tails""; ""4.8 Stable distributions with α close to extreme values""; ""4.9 Summary""; ""5 Integral transformations""; ""5.1 Laplace transformation""; ""5.2 Inversion of the Laplace transformation""; ""5.3 Tauberian theorems"". - ""5.4 One-sided stable distributions""""5.5 Laplace transformation of two-sided distributions""; ""5.6 The Mellin transformation""; ""5.7 The characteristic transformation""; ""5.8 The logarithmic moments""; ""5.9 Multiplication and division theorems""; ""6 Special functions and equations""; ""6.1 Integrodifferential equations""; ""6.2 The Laplace equation""; ""6.3 Fractional integrodifferential equations""; ""6.4 Splitting of the differential equations""; ""6.5 Some special cases""; ""6.6 The Whittaker functions""; ""6.7 Generalized incomplete hypergeometrical function"". - ""6.8 The Meijer and Fox functions""""6.9 Stable densities as a class of special functions""; ""6.10 Transstable functions""; ""6.11 Concluding remarks""; ""7 Multivariate stable laws""; ""7.1 Bivariate stable distributions""; ""7.2 Trivariate stable distributions""; ""7.3 Multivariate stable distributions""; ""7.4 Spherically symmetric multivariate distributions""; ""7.5 Spherically symmetric stable distributions""; ""8 Simulation""; ""8.1 The inverse function method""; ""8.2 The general formula""; ""8.3 Approximate algorithm for one-dimensional symmetric stable variables"". - ""8.4 Simulation of three-dimensional spherically symmetric stable vectors""
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| Emner | |
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| ISBN | 9067643017
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