Weak convergence and its applications /:
Weak convergence of stochastic processes is one of most important theories in probability theory. Not only probability experts but also more and more statisticians are interested in it. In the study of statistics and econometrics, some problems cannot be solved by the classical method. In this book,...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2014.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Weak convergence of stochastic processes is one of most important theories in probability theory. Not only probability experts but also more and more statisticians are interested in it. In the study of statistics and econometrics, some problems cannot be solved by the classical method. In this book, we will introduce some recent development of modern weak convergence theory to overcome defects of classical theory. |
| Beschreibung: | 1 online resource (viii, 176 pages) |
| Bibliographie: | Includes bibliographical references (pages 171-174) and index. |
| ISBN: | 9789814447706 9814447706 |
Internformat
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| 245 | 1 | 0 | |a Weak convergence and its applications / |c Zhengyan Lin, Hanchao Wang. |
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| 505 | 0 | |a 1. The definition and basic properties of weak convergence. 1.1. Metric space. 1.2. The definition of weak convergence of stochastic processes and portmanteau theorem. 1.3. How to verify the weak convergence? 1.4. Two examples of applications of weak convergence -- 2. Convergence to the independent increment processes. 2.1. The basic conditions of convergence to the Gaussian independent increment processes. 2.2. Donsker invariance principle. 2.3. Convergence of Poisson point processes. 2.4. Two examples of applications of point process method -- 3. Convergence to semimartingales. 3.1. The conditions of tightness for semimartingale sequence. 3.2. Weak convergence to semimartingale. 3.3. Weak convergence to stochastic integral I: the martingale convergence approach. 3.4. Weak convergence to stochastic integral II: Kurtz and Protter's approach. 3.5. Stable central limit theorem for semimartingales. 3.6. An application to stochastic differential equations -- 4. Convergence of empirical processes. 4.1. Classical weak convergence of empirical processes. 4.2. Weak convergence of marked empirical processes. 4.3. Weak convergence of function index empirical processes. 4.4. Weak convergence of empirical processes involving time-dependent data. 4.5. Two examples of applications in statistics. | |
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| contents | 1. The definition and basic properties of weak convergence. 1.1. Metric space. 1.2. The definition of weak convergence of stochastic processes and portmanteau theorem. 1.3. How to verify the weak convergence? 1.4. Two examples of applications of weak convergence -- 2. Convergence to the independent increment processes. 2.1. The basic conditions of convergence to the Gaussian independent increment processes. 2.2. Donsker invariance principle. 2.3. Convergence of Poisson point processes. 2.4. Two examples of applications of point process method -- 3. Convergence to semimartingales. 3.1. The conditions of tightness for semimartingale sequence. 3.2. Weak convergence to semimartingale. 3.3. Weak convergence to stochastic integral I: the martingale convergence approach. 3.4. Weak convergence to stochastic integral II: Kurtz and Protter's approach. 3.5. Stable central limit theorem for semimartingales. 3.6. An application to stochastic differential equations -- 4. Convergence of empirical processes. 4.1. Classical weak convergence of empirical processes. 4.2. Weak convergence of marked empirical processes. 4.3. Weak convergence of function index empirical processes. 4.4. Weak convergence of empirical processes involving time-dependent data. 4.5. Two examples of applications in statistics. |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:26:12Z |
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| institution_GND | http://id.loc.gov/authorities/names/no2001005546 |
| isbn | 9789814447706 9814447706 |
| language | English |
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| spelling | Lin, Zhengyan. Weak convergence and its applications / Zhengyan Lin, Hanchao Wang. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2014. 1 online resource (viii, 176 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 171-174) and index. 1. The definition and basic properties of weak convergence. 1.1. Metric space. 1.2. The definition of weak convergence of stochastic processes and portmanteau theorem. 1.3. How to verify the weak convergence? 1.4. Two examples of applications of weak convergence -- 2. Convergence to the independent increment processes. 2.1. The basic conditions of convergence to the Gaussian independent increment processes. 2.2. Donsker invariance principle. 2.3. Convergence of Poisson point processes. 2.4. Two examples of applications of point process method -- 3. Convergence to semimartingales. 3.1. The conditions of tightness for semimartingale sequence. 3.2. Weak convergence to semimartingale. 3.3. Weak convergence to stochastic integral I: the martingale convergence approach. 3.4. Weak convergence to stochastic integral II: Kurtz and Protter's approach. 3.5. Stable central limit theorem for semimartingales. 3.6. An application to stochastic differential equations -- 4. Convergence of empirical processes. 4.1. Classical weak convergence of empirical processes. 4.2. Weak convergence of marked empirical processes. 4.3. Weak convergence of function index empirical processes. 4.4. Weak convergence of empirical processes involving time-dependent data. 4.5. Two examples of applications in statistics. Weak convergence of stochastic processes is one of most important theories in probability theory. Not only probability experts but also more and more statisticians are interested in it. In the study of statistics and econometrics, some problems cannot be solved by the classical method. In this book, we will introduce some recent development of modern weak convergence theory to overcome defects of classical theory. Convergence. http://id.loc.gov/authorities/subjects/sh85031692 Distribution (Probability theory) http://id.loc.gov/authorities/subjects/sh85038545 Convergence (Mathématiques) Distribution (Théorie des probabilités) distribution (statistics-related concept) aat MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Convergence fast Distribution (Probability theory) fast Wang, Hanchao. World Scientific (Firm) http://id.loc.gov/authorities/names/no2001005546 Print version: 9789814447690 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=942142 Volltext |
| spellingShingle | Lin, Zhengyan Weak convergence and its applications / 1. The definition and basic properties of weak convergence. 1.1. Metric space. 1.2. The definition of weak convergence of stochastic processes and portmanteau theorem. 1.3. How to verify the weak convergence? 1.4. Two examples of applications of weak convergence -- 2. Convergence to the independent increment processes. 2.1. The basic conditions of convergence to the Gaussian independent increment processes. 2.2. Donsker invariance principle. 2.3. Convergence of Poisson point processes. 2.4. Two examples of applications of point process method -- 3. Convergence to semimartingales. 3.1. The conditions of tightness for semimartingale sequence. 3.2. Weak convergence to semimartingale. 3.3. Weak convergence to stochastic integral I: the martingale convergence approach. 3.4. Weak convergence to stochastic integral II: Kurtz and Protter's approach. 3.5. Stable central limit theorem for semimartingales. 3.6. An application to stochastic differential equations -- 4. Convergence of empirical processes. 4.1. Classical weak convergence of empirical processes. 4.2. Weak convergence of marked empirical processes. 4.3. Weak convergence of function index empirical processes. 4.4. Weak convergence of empirical processes involving time-dependent data. 4.5. Two examples of applications in statistics. Convergence. http://id.loc.gov/authorities/subjects/sh85031692 Distribution (Probability theory) http://id.loc.gov/authorities/subjects/sh85038545 Convergence (Mathématiques) Distribution (Théorie des probabilités) distribution (statistics-related concept) aat MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Convergence fast Distribution (Probability theory) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85031692 http://id.loc.gov/authorities/subjects/sh85038545 |
| title | Weak convergence and its applications / |
| title_auth | Weak convergence and its applications / |
| title_exact_search | Weak convergence and its applications / |
| title_full | Weak convergence and its applications / Zhengyan Lin, Hanchao Wang. |
| title_fullStr | Weak convergence and its applications / Zhengyan Lin, Hanchao Wang. |
| title_full_unstemmed | Weak convergence and its applications / Zhengyan Lin, Hanchao Wang. |
| title_short | Weak convergence and its applications / |
| title_sort | weak convergence and its applications |
| topic | Convergence. http://id.loc.gov/authorities/subjects/sh85031692 Distribution (Probability theory) http://id.loc.gov/authorities/subjects/sh85038545 Convergence (Mathématiques) Distribution (Théorie des probabilités) distribution (statistics-related concept) aat MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Convergence fast Distribution (Probability theory) fast |
| topic_facet | Convergence. Distribution (Probability theory) Convergence (Mathématiques) Distribution (Théorie des probabilités) distribution (statistics-related concept) MATHEMATICS Applied. MATHEMATICS Probability & Statistics General. Convergence |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=942142 |
| work_keys_str_mv | AT linzhengyan weakconvergenceanditsapplications AT wanghanchao weakconvergenceanditsapplications AT worldscientificfirm weakconvergenceanditsapplications |