| Description |
1 online resource (448 pages) |
| Series |
Advanced Series on Statistical Science and Applied Probability |
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Advanced series on statistical science & applied probability.
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| Contents |
Preface; 1. Random Systems with Covariance Inequalities; 1 Basic definitions and simple examples; 2 Classes of associated and related systems; 3 Random measures; 4 Association and probability measures on lattices; 5 Further extensions of dependence notions; 2. Moment and Maximal Inequalities; 1 Bounds for partial sums in the Lp space; 2 Results based on supermodular order; 3 Rosenthal-type inequalities; 4 Estimates for the distribution functions of partial maxima; 3. Central Limit Theorem; 1 Sufficient conditions for normal approximation; 2 The Newman conjecture |
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3 Sharp rates of normal approximation4. Almost Sure Convergence; 1 Strong law of large numbers; 2 Rate of convergence in the LLN; 3 Almost sure Gaussian approximation; 5. Invariance Principles; 1 Weak invariance principle; 2 Strong invariance principle; 6. Law of the Iterated Logarithm; 1 Extensions of the classical LIL; 2 Functional LIL; 3 Law of a single logarithm; 7. Statistical Applications; 1 Statistics involving random normalization; 2 Kernel density estimation; 3 Empirical processes; 8. Integral Functionals; 1 Stationary associated measures; 2 PDE with random initial data |
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3 Asymptotical behavior of transformed solutions of the Burgers equationAppendix A Auxiliary Statements; A.1 Extensions of the Hoe ding lemma; A.2 Markov processes. Background; A.3 Poisson spatial process; A.4 Electric currents; A.5 The Moricz theorem; A.6 Gaussian approximation; Bibliography; Notation Index; Subject Index |
| Summary |
This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, |
| Bibliography |
Includes bibliographical references (pages 411-430) and indexes |
| Notes |
Print version record |
| Subject |
Limit theorems (Probability theory)
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Random fields.
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Limit theorems (Probability theory)
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Random fields
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| Form |
Electronic book
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| Author |
Shashkin, A. P. (Alekseĭ Pavlovich)
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| ISBN |
9789812709417 |
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981270941X |
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