Generalized poisson models and their applications in insurance and finance /
| Основен автор: | Bening, Vladimir E. |
|---|---|
| Други автори: | Korolev, Victor Yu. |
| Формат: | Електронна книга |
| Език: | English |
| Публикувано: |
Utrecht ; Boston :
VSP,
2002.
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| Серия: |
Modern probability and statistics.
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| Предмети: | |
| Онлайн достъп: |
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=629197 |
| Подобни документи: |
Print version::
Generalized poisson models and their applications in insurance and finance |
Съдържание:
- ""Contents""; ""Foreword""; ""Preface""; ""1 Basic notions of probability theory""; ""1.1 Random variables, their distributions and moments""; ""1.2 Generating and characteristic functions""; ""1.3 Random vectors. Stochastic independence""; ""1.4 Weak convergence of random variables and distribution functions""; ""1.5 Poisson theorem""; ""1.6 Law of large numbers. Central limit theorem. Stable laws""; ""1.7 The Berry-Esseen inequality""; ""1.8 Asymptotic expansions in the central limit theorem""; ""1.9 Elementary properties of random sums""; ""1.10 Stochastic processes""
- ""2 Poisson process""""2.1 The definition and elementary properties of a Poisson process""; ""2.2 Poisson process as a model of chaotic displacement of points in time""; ""2.3 The asymptotic normality of a Poisson process""; ""2.4 Elementary rarefaction of renewal processes""; ""3 Convergence of superpositions of independent stochastic processes""; ""3.1 Characteristic features of the problem""; ""3.2 Approximation of distributions of randomly indexed random sequences by special mixtures""
- ""3.3 The transfer theorem. Relations between the limit laws for random sequences with random and non-random indices""""3.4 Necessary and sufficient conditions for the convergence of distributions of random sequences with independent random indices""; ""3.5 Convergence of distributions of randomly indexed sequences to identifiable location or scale mixtures. The asymptotic behavior of extremal random sums""; ""3.6 Convergence of distributions of random sums. The central limit theorem and the law of large numbers for random sums""
- ""3.7 A general theorem on the asymptotic behavior of superpositions of independent stochastic processes""""3.8 The transfer theorem for random sums of independent identically distributed random variables in the double array limit scheme""; ""4 Compound Poisson distributions""; ""4.1 Mixed and compound Poisson distributions""; ""4.2 Discrete compound Poisson distributions""; ""4.3 The asymptotic normality of compound Poisson distributions. The Berry-Esseen inequality for Poisson random sums. Non-central Lyapunov fractions""; ""4.4 Asymptotic expansions for compound Poisson distributions""
- ""4.5 The asymptotic expansions for the quantiles of compound Poisson distributions""""4.6 Exponential inequalities for the probabilities of large deviations of Poisson random sums. An analog of Bernshtein-Kolmogorov inequality""; ""4.7 The application of Esscher transforms to the approximation of the tails of compound Poisson distributions""; ""4.8 Estimates of convergence rate in local limit theorems for Poisson random sums""; ""5 Classical risk processes""; ""5.1 The definition of the classical risk process. Its asymptotic normality""