Limit Theorems for Random Fields with Singular Spectrum:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1999
|
| Series: | Mathematics and Its Applications
465 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This book is devoted to an investigation of the basic problems of the the ory of random fields which are characterized by certain singular properties (e. g., unboundedness, or vanishing) of their spectral densities. These ran dom fields are called, the random fields with singular spectrum, long-memory fields, random fields with long-range dependence, fields with slowly decaying correlations or strongly dependent random fields by various authors. This phenomenon has been observed empirically by many scientists long before suitable mathematical models were known. The methods and results differ significantly from the theory of weakly dependent random fields. The first chapter presents basic concepts of the spectral theory of random fields, some examples of random processes and fields with singular spectrum, Tauberian and Abelian theorems for the covariance function of singular ran dom fields. In the second chapter limit theorems for non-linear functionals of random fields with singular spectrum are proved. Chapter 3 summarizes some limit theorems for geometric functionals of random fields with long-range dependence. Limit distributions of the solutions of Burgers equation with random data via parabolic and hyperbolic rescaling are presented in chapter 4. And chapter 5 presents some problems of statistical analysis of random fields with singular spectrum. I would like to thank the editor, Michiel Hazewinkel, for his support. I am grateful to the following students and colleagues: 1. Deriev, A. Olenko, K. Rybasov, L. Sakhno, M. Sharapov, A. Sikorskii, M. Silac-BenSic. I would also like to thank V.Anh, O. Barndorff-Nielsen,Yu. Belyaev, P. |
| Physical Description: | 1 Online-Ressource (VIII, 406 p) |
| ISBN: | 9789401146074 9789401059473 |
| DOI: | 10.1007/978-94-011-4607-4 |
Staff View
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| id | DE-604.BV042423948 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401146074 9789401059473 |
| language | English |
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| spelling | Leonenko, Nikolai Verfasser aut Limit Theorems for Random Fields with Singular Spectrum by Nikolai Leonenko Dordrecht Springer Netherlands 1999 1 Online-Ressource (VIII, 406 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 465 This book is devoted to an investigation of the basic problems of the the ory of random fields which are characterized by certain singular properties (e. g., unboundedness, or vanishing) of their spectral densities. These ran dom fields are called, the random fields with singular spectrum, long-memory fields, random fields with long-range dependence, fields with slowly decaying correlations or strongly dependent random fields by various authors. This phenomenon has been observed empirically by many scientists long before suitable mathematical models were known. The methods and results differ significantly from the theory of weakly dependent random fields. The first chapter presents basic concepts of the spectral theory of random fields, some examples of random processes and fields with singular spectrum, Tauberian and Abelian theorems for the covariance function of singular ran dom fields. In the second chapter limit theorems for non-linear functionals of random fields with singular spectrum are proved. Chapter 3 summarizes some limit theorems for geometric functionals of random fields with long-range dependence. Limit distributions of the solutions of Burgers equation with random data via parabolic and hyperbolic rescaling are presented in chapter 4. And chapter 5 presents some problems of statistical analysis of random fields with singular spectrum. I would like to thank the editor, Michiel Hazewinkel, for his support. I am grateful to the following students and colleagues: 1. Deriev, A. Olenko, K. Rybasov, L. Sakhno, M. Sharapov, A. Sikorskii, M. Silac-BenSic. I would also like to thank V.Anh, O. Barndorff-Nielsen,Yu. Belyaev, P. Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Fluid- and Aerodynamics Applications of Mathematics Mathematik Statistik https://doi.org/10.1007/978-94-011-4607-4 Verlag Volltext |
| spellingShingle | Leonenko, Nikolai Limit Theorems for Random Fields with Singular Spectrum Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Fluid- and Aerodynamics Applications of Mathematics Mathematik Statistik |
| title | Limit Theorems for Random Fields with Singular Spectrum |
| title_auth | Limit Theorems for Random Fields with Singular Spectrum |
| title_exact_search | Limit Theorems for Random Fields with Singular Spectrum |
| title_full | Limit Theorems for Random Fields with Singular Spectrum by Nikolai Leonenko |
| title_fullStr | Limit Theorems for Random Fields with Singular Spectrum by Nikolai Leonenko |
| title_full_unstemmed | Limit Theorems for Random Fields with Singular Spectrum by Nikolai Leonenko |
| title_short | Limit Theorems for Random Fields with Singular Spectrum |
| title_sort | limit theorems for random fields with singular spectrum |
| topic | Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Fluid- and Aerodynamics Applications of Mathematics Mathematik Statistik |
| topic_facet | Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Fluid- and Aerodynamics Applications of Mathematics Mathematik Statistik |
| url | https://doi.org/10.1007/978-94-011-4607-4 |
| work_keys_str_mv | AT leonenkonikolai limittheoremsforrandomfieldswithsingularspectrum |