Derivation and Martingales:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1970
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
49 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g. , the interval basis) are studied. The principal tool is a Vitali property, whose precise form depends on the derivation property studied. The "halo" (defined at the beginning of Part I, Ch. IV) properties can serve to establish a Vitali property, or sometimes produce directly a derivation property. The main results established are the theorem of JESSEN-MARCINKIEWICZ-ZYGMUND (Part I, Ch. V) and the theorem of A. P. MORSE on the universal derivability of star blankets (Ch. VI) . . In Part II, points are at first discarded; the setting is somatic. It opens by treating an increasing stochastic basis with directed index sets (Th. I. 3) on which premartingales, semimartingales and martingales are defined. Convergence theorems, due largely to K. KRICKEBERG, are obtained using various types of convergence: stochastic, in the mean, in Lp-spaces, in ORLICZ spaces, and according to the order relation. We may mention in particular Th. II. 4. 7 on the stochastic convergence of a submartingale of bounded variation. To each theorem for martingales and semi-martingales there corresponds a theorem in the atomic case in the theory of cell (abstract interval) functions. The derivates concerned are global. Finally, in Ch |
| Beschreibung: | 1 Online-Ressource (VIII, 206 p.) 1 illus |
| ISBN: | 9783642861802 9783642861826 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-86180-2 |
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Datensatz im Suchindex
| _version_ | 1804153098373955584 |
|---|---|
| any_adam_object | |
| author | Hayes, Charles A. |
| author_facet | Hayes, Charles A. |
| author_role | aut |
| author_sort | Hayes, Charles A. |
| author_variant | c a h ca cah |
| building | Verbundindex |
| bvnumber | BV042423059 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1185213112 (DE-599)BVBBV042423059 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-86180-2 |
| format | Electronic eBook |
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| id | DE-604.BV042423059 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642861802 9783642861826 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858476 |
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| physical | 1 Online-Ressource (VIII, 206 p.) 1 illus |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1970 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Hayes, Charles A. Verfasser aut Derivation and Martingales by Charles A. Hayes, Christian Y. Pauc Berlin, Heidelberg Springer Berlin Heidelberg 1970 1 Online-Ressource (VIII, 206 p.) 1 illus txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 49 0071-1136 In Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g. , the interval basis) are studied. The principal tool is a Vitali property, whose precise form depends on the derivation property studied. The "halo" (defined at the beginning of Part I, Ch. IV) properties can serve to establish a Vitali property, or sometimes produce directly a derivation property. The main results established are the theorem of JESSEN-MARCINKIEWICZ-ZYGMUND (Part I, Ch. V) and the theorem of A. P. MORSE on the universal derivability of star blankets (Ch. VI) . . In Part II, points are at first discarded; the setting is somatic. It opens by treating an increasing stochastic basis with directed index sets (Th. I. 3) on which premartingales, semimartingales and martingales are defined. Convergence theorems, due largely to K. KRICKEBERG, are obtained using various types of convergence: stochastic, in the mean, in Lp-spaces, in ORLICZ spaces, and according to the order relation. We may mention in particular Th. II. 4. 7 on the stochastic convergence of a submartingale of bounded variation. To each theorem for martingales and semi-martingales there corresponds a theorem in the atomic case in the theory of cell (abstract interval) functions. The derivates concerned are global. Finally, in Ch Mathematics Mathematics, general Mathematik Derivation Algebra (DE-588)4134656-7 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Ableitung Infinitesimalrechnung (DE-588)4233840-2 gnd rswk-swf Differentiation Mathematik (DE-588)4149787-9 gnd rswk-swf Martingal (DE-588)4126466-6 s Ableitung Infinitesimalrechnung (DE-588)4233840-2 s 1\p DE-604 Differentiation Mathematik (DE-588)4149787-9 s Theorie (DE-588)4059787-8 s 2\p DE-604 Derivation Algebra (DE-588)4134656-7 s 3\p DE-604 Pauc, Christian Y. Sonstige oth https://doi.org/10.1007/978-3-642-86180-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hayes, Charles A. Derivation and Martingales Mathematics Mathematics, general Mathematik Derivation Algebra (DE-588)4134656-7 gnd Theorie (DE-588)4059787-8 gnd Martingal (DE-588)4126466-6 gnd Ableitung Infinitesimalrechnung (DE-588)4233840-2 gnd Differentiation Mathematik (DE-588)4149787-9 gnd |
| subject_GND | (DE-588)4134656-7 (DE-588)4059787-8 (DE-588)4126466-6 (DE-588)4233840-2 (DE-588)4149787-9 |
| title | Derivation and Martingales |
| title_auth | Derivation and Martingales |
| title_exact_search | Derivation and Martingales |
| title_full | Derivation and Martingales by Charles A. Hayes, Christian Y. Pauc |
| title_fullStr | Derivation and Martingales by Charles A. Hayes, Christian Y. Pauc |
| title_full_unstemmed | Derivation and Martingales by Charles A. Hayes, Christian Y. Pauc |
| title_short | Derivation and Martingales |
| title_sort | derivation and martingales |
| topic | Mathematics Mathematics, general Mathematik Derivation Algebra (DE-588)4134656-7 gnd Theorie (DE-588)4059787-8 gnd Martingal (DE-588)4126466-6 gnd Ableitung Infinitesimalrechnung (DE-588)4233840-2 gnd Differentiation Mathematik (DE-588)4149787-9 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Derivation Algebra Theorie Martingal Ableitung Infinitesimalrechnung Differentiation Mathematik |
| url | https://doi.org/10.1007/978-3-642-86180-2 |
| work_keys_str_mv | AT hayescharlesa derivationandmartingales AT paucchristiany derivationandmartingales |