Random and vector measures /:
The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new resul...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore :
World Scientific,
©2012.
|
| Schriftenreihe: | Series on multivariate analysis ;
v. 9. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new results are included and many research avenues are opened up. |
| Beschreibung: | 1 online resource (xiii, 538 pages) |
| Bibliographie: | Includes bibliographical references (pages 497-521) and index. |
| ISBN: | 9789814350822 9814350826 |
Internformat
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| 505 | 0 | |a 1. Introduction and motivation. 1.1. Introducing vector valued measures. 1.2. Basic structures. 1.3. Additivity properties of vector valued measures. 1.4. Complements and exercises -- 2. Second order random measures and representations. 2.1. Introduction. 2.2. Structures of second order random measures. 2.3. Shift invariant second order random measures. 2.4. A specialization of random measures invariant on subgroups. 2.5. Complements and exercises -- 3. Random measures admitting controls. 3.1. Structural analysis. 3.2. Controls for weakly stable random measures. 3.3. Integral representations of stable classes by random measures. 3.4. Integral representations of some second order processes. 3.5. Complements and exercises -- 4. Random measures in Hilbert space : specialized analysis. 4.1. Bilinear functionals associated with random measures. 4.2. Local classes of random fields and related measures. 4.3. Bilinear forms and random measures. 4.4. Random measures with constraints. 4.5. Complements and exercises -- 5. More on random measures and integrals. 5.1. Random measures, bimeasures and convolutions. 5.2. Bilinear forms and random measure algebras. 5.3. Vector integrands and integrals with stable random measures. 5.4. Positive and other special classes of random measures. 5.5. Complements and exercises -- 6. Martingale type measures and their integrals. 6.1. Random measures and deterministic integrands. 6.2. Random measures and stochastic integrands. 6.3. Random measures, stopping times and stochastic integration. 6.4. Generalizations of Martingale integrals. 6.5. Complements and exercises -- 7. Multiple random measures and integrals. 7.1. Basic quasimartingale spaces and integrals. 7.2. Multiple random measures, Part I : Cartesian products. 7.3. Multiple random measures, Part II :Noncartesian products. 7.4. Random line integrals with Fubini and Green-Stokes theorems. 7.5. Random measures on partially ordered sets. 7.6. Multiple random integrals using white noise methods. 7.7. Complements and exercises -- 8. Vector measures and integrals. 8.1. Vector measures of nonfinite variation. 8.2. Vector integration with measures of finite semivariation, Part I. 8.3. Vector integration with measures of finite semivariation, Part II. 8.4. Some applications of vector measure integration, Part I. 8.5. Some applications of vector measure integration, Part II. 8.6. Complements and exercises -- 9. Random and vector multimeasures. 9.1. Bimeasures and multiple integrals. 9.2. Bimeasure domination, dilations and representations of processes. 9.3. Spectral analysis of second order fields and bimeasures. 9.4. Multimeasures and multilinear forms. 9.5. Complements and exercises. | |
| 520 | |a The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new results are included and many research avenues are opened up. | ||
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| 650 | 6 | |a Mesures aléatoires. | |
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| 650 | 7 | |a Random measures |2 fast | |
| 650 | 7 | |a Vector-valued measures |2 fast | |
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| author | Rao, M. M. (Malempati Madhusudana), 1929- |
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| contents | 1. Introduction and motivation. 1.1. Introducing vector valued measures. 1.2. Basic structures. 1.3. Additivity properties of vector valued measures. 1.4. Complements and exercises -- 2. Second order random measures and representations. 2.1. Introduction. 2.2. Structures of second order random measures. 2.3. Shift invariant second order random measures. 2.4. A specialization of random measures invariant on subgroups. 2.5. Complements and exercises -- 3. Random measures admitting controls. 3.1. Structural analysis. 3.2. Controls for weakly stable random measures. 3.3. Integral representations of stable classes by random measures. 3.4. Integral representations of some second order processes. 3.5. Complements and exercises -- 4. Random measures in Hilbert space : specialized analysis. 4.1. Bilinear functionals associated with random measures. 4.2. Local classes of random fields and related measures. 4.3. Bilinear forms and random measures. 4.4. Random measures with constraints. 4.5. Complements and exercises -- 5. More on random measures and integrals. 5.1. Random measures, bimeasures and convolutions. 5.2. Bilinear forms and random measure algebras. 5.3. Vector integrands and integrals with stable random measures. 5.4. Positive and other special classes of random measures. 5.5. Complements and exercises -- 6. Martingale type measures and their integrals. 6.1. Random measures and deterministic integrands. 6.2. Random measures and stochastic integrands. 6.3. Random measures, stopping times and stochastic integration. 6.4. Generalizations of Martingale integrals. 6.5. Complements and exercises -- 7. Multiple random measures and integrals. 7.1. Basic quasimartingale spaces and integrals. 7.2. Multiple random measures, Part I : Cartesian products. 7.3. Multiple random measures, Part II :Noncartesian products. 7.4. Random line integrals with Fubini and Green-Stokes theorems. 7.5. Random measures on partially ordered sets. 7.6. Multiple random integrals using white noise methods. 7.7. Complements and exercises -- 8. Vector measures and integrals. 8.1. Vector measures of nonfinite variation. 8.2. Vector integration with measures of finite semivariation, Part I. 8.3. Vector integration with measures of finite semivariation, Part II. 8.4. Some applications of vector measure integration, Part I. 8.5. Some applications of vector measure integration, Part II. 8.6. Complements and exercises -- 9. Random and vector multimeasures. 9.1. Bimeasures and multiple integrals. 9.2. Bimeasure domination, dilations and representations of processes. 9.3. Spectral analysis of second order fields and bimeasures. 9.4. Multimeasures and multilinear forms. 9.5. Complements and exercises. |
| ctrlnum | (OCoLC)776201892 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn776201892 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:15Z |
| institution | BVB |
| isbn | 9789814350822 9814350826 |
| language | English |
| oclc_num | 776201892 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 538 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific, |
| record_format | marc |
| series | Series on multivariate analysis ; |
| series2 | Series on multivariate analysis ; |
| spelling | Rao, M. M. (Malempati Madhusudana), 1929- https://id.oclc.org/worldcat/entity/E39PBJjCM8PRBJHCYJTvjWH6Kd http://id.loc.gov/authorities/names/n79115176 Random and vector measures / M.M. Rao. Singapore : World Scientific, ©2012. 1 online resource (xiii, 538 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on multivariate analysis ; v. 9 Includes bibliographical references (pages 497-521) and index. Print version record. 1. Introduction and motivation. 1.1. Introducing vector valued measures. 1.2. Basic structures. 1.3. Additivity properties of vector valued measures. 1.4. Complements and exercises -- 2. Second order random measures and representations. 2.1. Introduction. 2.2. Structures of second order random measures. 2.3. Shift invariant second order random measures. 2.4. A specialization of random measures invariant on subgroups. 2.5. Complements and exercises -- 3. Random measures admitting controls. 3.1. Structural analysis. 3.2. Controls for weakly stable random measures. 3.3. Integral representations of stable classes by random measures. 3.4. Integral representations of some second order processes. 3.5. Complements and exercises -- 4. Random measures in Hilbert space : specialized analysis. 4.1. Bilinear functionals associated with random measures. 4.2. Local classes of random fields and related measures. 4.3. Bilinear forms and random measures. 4.4. Random measures with constraints. 4.5. Complements and exercises -- 5. More on random measures and integrals. 5.1. Random measures, bimeasures and convolutions. 5.2. Bilinear forms and random measure algebras. 5.3. Vector integrands and integrals with stable random measures. 5.4. Positive and other special classes of random measures. 5.5. Complements and exercises -- 6. Martingale type measures and their integrals. 6.1. Random measures and deterministic integrands. 6.2. Random measures and stochastic integrands. 6.3. Random measures, stopping times and stochastic integration. 6.4. Generalizations of Martingale integrals. 6.5. Complements and exercises -- 7. Multiple random measures and integrals. 7.1. Basic quasimartingale spaces and integrals. 7.2. Multiple random measures, Part I : Cartesian products. 7.3. Multiple random measures, Part II :Noncartesian products. 7.4. Random line integrals with Fubini and Green-Stokes theorems. 7.5. Random measures on partially ordered sets. 7.6. Multiple random integrals using white noise methods. 7.7. Complements and exercises -- 8. Vector measures and integrals. 8.1. Vector measures of nonfinite variation. 8.2. Vector integration with measures of finite semivariation, Part I. 8.3. Vector integration with measures of finite semivariation, Part II. 8.4. Some applications of vector measure integration, Part I. 8.5. Some applications of vector measure integration, Part II. 8.6. Complements and exercises -- 9. Random and vector multimeasures. 9.1. Bimeasures and multiple integrals. 9.2. Bimeasure domination, dilations and representations of processes. 9.3. Spectral analysis of second order fields and bimeasures. 9.4. Multimeasures and multilinear forms. 9.5. Complements and exercises. The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new results are included and many research avenues are opened up. Vector-valued measures. http://id.loc.gov/authorities/subjects/sh85142458 Random measures. http://id.loc.gov/authorities/subjects/sh94002187 Mesures vectorielles. Mesures aléatoires. MATHEMATICS Functional Analysis. bisacsh Random measures fast Vector-valued measures fast Print version: Rao, M.M. (Malempati Madhusudana), 1929- Random and vector measures. Singapore : World Scientific, ©2012 9789814350815 (OCoLC)707968895 Series on multivariate analysis ; v. 9. http://id.loc.gov/authorities/names/n95093809 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426431 Volltext |
| spellingShingle | Rao, M. M. (Malempati Madhusudana), 1929- Random and vector measures / Series on multivariate analysis ; 1. Introduction and motivation. 1.1. Introducing vector valued measures. 1.2. Basic structures. 1.3. Additivity properties of vector valued measures. 1.4. Complements and exercises -- 2. Second order random measures and representations. 2.1. Introduction. 2.2. Structures of second order random measures. 2.3. Shift invariant second order random measures. 2.4. A specialization of random measures invariant on subgroups. 2.5. Complements and exercises -- 3. Random measures admitting controls. 3.1. Structural analysis. 3.2. Controls for weakly stable random measures. 3.3. Integral representations of stable classes by random measures. 3.4. Integral representations of some second order processes. 3.5. Complements and exercises -- 4. Random measures in Hilbert space : specialized analysis. 4.1. Bilinear functionals associated with random measures. 4.2. Local classes of random fields and related measures. 4.3. Bilinear forms and random measures. 4.4. Random measures with constraints. 4.5. Complements and exercises -- 5. More on random measures and integrals. 5.1. Random measures, bimeasures and convolutions. 5.2. Bilinear forms and random measure algebras. 5.3. Vector integrands and integrals with stable random measures. 5.4. Positive and other special classes of random measures. 5.5. Complements and exercises -- 6. Martingale type measures and their integrals. 6.1. Random measures and deterministic integrands. 6.2. Random measures and stochastic integrands. 6.3. Random measures, stopping times and stochastic integration. 6.4. Generalizations of Martingale integrals. 6.5. Complements and exercises -- 7. Multiple random measures and integrals. 7.1. Basic quasimartingale spaces and integrals. 7.2. Multiple random measures, Part I : Cartesian products. 7.3. Multiple random measures, Part II :Noncartesian products. 7.4. Random line integrals with Fubini and Green-Stokes theorems. 7.5. Random measures on partially ordered sets. 7.6. Multiple random integrals using white noise methods. 7.7. Complements and exercises -- 8. Vector measures and integrals. 8.1. Vector measures of nonfinite variation. 8.2. Vector integration with measures of finite semivariation, Part I. 8.3. Vector integration with measures of finite semivariation, Part II. 8.4. Some applications of vector measure integration, Part I. 8.5. Some applications of vector measure integration, Part II. 8.6. Complements and exercises -- 9. Random and vector multimeasures. 9.1. Bimeasures and multiple integrals. 9.2. Bimeasure domination, dilations and representations of processes. 9.3. Spectral analysis of second order fields and bimeasures. 9.4. Multimeasures and multilinear forms. 9.5. Complements and exercises. Vector-valued measures. http://id.loc.gov/authorities/subjects/sh85142458 Random measures. http://id.loc.gov/authorities/subjects/sh94002187 Mesures vectorielles. Mesures aléatoires. MATHEMATICS Functional Analysis. bisacsh Random measures fast Vector-valued measures fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85142458 http://id.loc.gov/authorities/subjects/sh94002187 |
| title | Random and vector measures / |
| title_auth | Random and vector measures / |
| title_exact_search | Random and vector measures / |
| title_full | Random and vector measures / M.M. Rao. |
| title_fullStr | Random and vector measures / M.M. Rao. |
| title_full_unstemmed | Random and vector measures / M.M. Rao. |
| title_short | Random and vector measures / |
| title_sort | random and vector measures |
| topic | Vector-valued measures. http://id.loc.gov/authorities/subjects/sh85142458 Random measures. http://id.loc.gov/authorities/subjects/sh94002187 Mesures vectorielles. Mesures aléatoires. MATHEMATICS Functional Analysis. bisacsh Random measures fast Vector-valued measures fast |
| topic_facet | Vector-valued measures. Random measures. Mesures vectorielles. Mesures aléatoires. MATHEMATICS Functional Analysis. Random measures Vector-valued measures |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426431 |
| work_keys_str_mv | AT raomm randomandvectormeasures |