A Compactness Principle for Bounded Sequences of Martingales with Applications View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1999

AUTHORS

F. Delbaen , W. Schachermayer

ABSTRACT

For H1-bounded sequences of martingales, we introduce a technique, related to the Kadeč-Pełczynski-decomposition for L1 sequences, that allows us to prove compactness theorems. Roughly speaking, a bounded sequence in H1 can be split into two sequences, one of which is weakly compact, the other forms the singular part. If the martingales are continuous then the singular part tends to zero in the semi-martingale topology. In the general case the singular parts give rise to a process of bounded variation. The technique allows to give a new proof of the Optional Decomposition Theorem in Mathematical Finance. More... »

PAGES

137-173

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-8681-9_10

DOI

http://dx.doi.org/10.1007/978-3-0348-8681-9_10

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1014650089


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Departement f\u00fcr Mathematik, ETH-Zentrum, CH-8092, Z\u00fcrich, Switzerland", 
          "id": "http://www.grid.ac/institutes/grid.5801.c", 
          "name": [
            "Departement f\u00fcr Mathematik, ETH-Zentrum, CH-8092, Z\u00fcrich, Switzerland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Delbaen", 
        "givenName": "F.", 
        "id": "sg:person.016436526230.58", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016436526230.58"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Abteilung f\u00fcr Finanz- und Versicherungsmathematik, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria", 
          "id": "http://www.grid.ac/institutes/grid.5329.d", 
          "name": [
            "Abteilung f\u00fcr Finanz- und Versicherungsmathematik, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Schachermayer", 
        "givenName": "W.", 
        "id": "sg:person.010531035430.26", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010531035430.26"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1999", 
    "datePublishedReg": "1999-01-01", 
    "description": "For H1-bounded sequences of martingales, we introduce a technique, related to the Kade\u010d-Pe\u0142czynski-decomposition for L1 sequences, that allows us to prove compactness theorems. Roughly speaking, a bounded sequence in H1 can be split into two sequences, one of which is weakly compact, the other forms the singular part. If the martingales are continuous then the singular part tends to zero in the semi-martingale topology. In the general case the singular parts give rise to a process of bounded variation. The technique allows to give a new proof of the Optional Decomposition Theorem in Mathematical Finance.", 
    "editor": [
      {
        "familyName": "Dalang", 
        "givenName": "Robert C.", 
        "type": "Person"
      }, 
      {
        "familyName": "Dozzi", 
        "givenName": "Marco", 
        "type": "Person"
      }, 
      {
        "familyName": "Russo", 
        "givenName": "Francesco", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-0348-8681-9_10", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-0348-9727-3", 
        "978-3-0348-8681-9"
      ], 
      "name": "Seminar on Stochastic Analysis, Random Fields and Applications", 
      "type": "Book"
    }, 
    "keywords": [
      "singular part", 
      "optional decomposition theorem", 
      "mathematical finance", 
      "compactness theorem", 
      "decomposition theorem", 
      "general case", 
      "compactness principle", 
      "martingales", 
      "new proof", 
      "bounded sequences", 
      "theorem", 
      "topology", 
      "proof", 
      "technique", 
      "decomposition", 
      "principles", 
      "applications", 
      "sequence", 
      "form", 
      "cases", 
      "finance", 
      "part", 
      "variation", 
      "process", 
      "rise", 
      "H1", 
      "L1 sequences"
    ], 
    "name": "A Compactness Principle for Bounded Sequences of Martingales with Applications", 
    "pagination": "137-173", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1014650089"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-0348-8681-9_10"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-0348-8681-9_10", 
      "https://app.dimensions.ai/details/publication/pub.1014650089"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-12-01T06:48", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221201/entities/gbq_results/chapter/chapter_218.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-0348-8681-9_10"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8681-9_10'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8681-9_10'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8681-9_10'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8681-9_10'


 

This table displays all metadata directly associated to this object as RDF triples.

106 TRIPLES      22 PREDICATES      52 URIs      45 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-0348-8681-9_10 schema:about anzsrc-for:01
2 anzsrc-for:0102
3 schema:author Naa37e087ca7549bab302498d4530f344
4 schema:datePublished 1999
5 schema:datePublishedReg 1999-01-01
6 schema:description For H1-bounded sequences of martingales, we introduce a technique, related to the Kadeč-Pełczynski-decomposition for L1 sequences, that allows us to prove compactness theorems. Roughly speaking, a bounded sequence in H1 can be split into two sequences, one of which is weakly compact, the other forms the singular part. If the martingales are continuous then the singular part tends to zero in the semi-martingale topology. In the general case the singular parts give rise to a process of bounded variation. The technique allows to give a new proof of the Optional Decomposition Theorem in Mathematical Finance.
7 schema:editor N759291f5cc5b49648394aee2bc44f4ac
8 schema:genre chapter
9 schema:isAccessibleForFree false
10 schema:isPartOf N7c354aaf224546e4ad4ab7fb6b18da38
11 schema:keywords H1
12 L1 sequences
13 applications
14 bounded sequences
15 cases
16 compactness principle
17 compactness theorem
18 decomposition
19 decomposition theorem
20 finance
21 form
22 general case
23 martingales
24 mathematical finance
25 new proof
26 optional decomposition theorem
27 part
28 principles
29 process
30 proof
31 rise
32 sequence
33 singular part
34 technique
35 theorem
36 topology
37 variation
38 schema:name A Compactness Principle for Bounded Sequences of Martingales with Applications
39 schema:pagination 137-173
40 schema:productId N63b45b3479cc461bb4d6cc8e876b679f
41 Na793238f672b442aadf1c6412241d836
42 schema:publisher Ne752c663b8fc4d639522ed05a4c2e200
43 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014650089
44 https://doi.org/10.1007/978-3-0348-8681-9_10
45 schema:sdDatePublished 2022-12-01T06:48
46 schema:sdLicense https://scigraph.springernature.com/explorer/license/
47 schema:sdPublisher N3a7b749be7604720a17c1259bf24991f
48 schema:url https://doi.org/10.1007/978-3-0348-8681-9_10
49 sgo:license sg:explorer/license/
50 sgo:sdDataset chapters
51 rdf:type schema:Chapter
52 N3a7b749be7604720a17c1259bf24991f schema:name Springer Nature - SN SciGraph project
53 rdf:type schema:Organization
54 N62eb52707bb6485982f9078c92914843 rdf:first N8a82ce5cb3674f8e8cfa36f70e930b98
55 rdf:rest rdf:nil
56 N63b45b3479cc461bb4d6cc8e876b679f schema:name doi
57 schema:value 10.1007/978-3-0348-8681-9_10
58 rdf:type schema:PropertyValue
59 N759291f5cc5b49648394aee2bc44f4ac rdf:first N8a43293416e844bf87bde4cc462d10a0
60 rdf:rest Nda6a5eb60859400d9d5c906ae72936c9
61 N7c354aaf224546e4ad4ab7fb6b18da38 schema:isbn 978-3-0348-8681-9
62 978-3-0348-9727-3
63 schema:name Seminar on Stochastic Analysis, Random Fields and Applications
64 rdf:type schema:Book
65 N8a43293416e844bf87bde4cc462d10a0 schema:familyName Dalang
66 schema:givenName Robert C.
67 rdf:type schema:Person
68 N8a82ce5cb3674f8e8cfa36f70e930b98 schema:familyName Russo
69 schema:givenName Francesco
70 rdf:type schema:Person
71 Na793238f672b442aadf1c6412241d836 schema:name dimensions_id
72 schema:value pub.1014650089
73 rdf:type schema:PropertyValue
74 Naa37e087ca7549bab302498d4530f344 rdf:first sg:person.016436526230.58
75 rdf:rest Nea48455a91104240b2d2d482968c55db
76 Nbe2611b695bf44109e3804f9b3df8047 schema:familyName Dozzi
77 schema:givenName Marco
78 rdf:type schema:Person
79 Nda6a5eb60859400d9d5c906ae72936c9 rdf:first Nbe2611b695bf44109e3804f9b3df8047
80 rdf:rest N62eb52707bb6485982f9078c92914843
81 Ne752c663b8fc4d639522ed05a4c2e200 schema:name Springer Nature
82 rdf:type schema:Organisation
83 Nea48455a91104240b2d2d482968c55db rdf:first sg:person.010531035430.26
84 rdf:rest rdf:nil
85 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
86 schema:name Mathematical Sciences
87 rdf:type schema:DefinedTerm
88 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
89 schema:name Applied Mathematics
90 rdf:type schema:DefinedTerm
91 sg:person.010531035430.26 schema:affiliation grid-institutes:grid.5329.d
92 schema:familyName Schachermayer
93 schema:givenName W.
94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010531035430.26
95 rdf:type schema:Person
96 sg:person.016436526230.58 schema:affiliation grid-institutes:grid.5801.c
97 schema:familyName Delbaen
98 schema:givenName F.
99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016436526230.58
100 rdf:type schema:Person
101 grid-institutes:grid.5329.d schema:alternateName Abteilung für Finanz- und Versicherungsmathematik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria
102 schema:name Abteilung für Finanz- und Versicherungsmathematik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria
103 rdf:type schema:Organization
104 grid-institutes:grid.5801.c schema:alternateName Departement für Mathematik, ETH-Zentrum, CH-8092, Zürich, Switzerland
105 schema:name Departement für Mathematik, ETH-Zentrum, CH-8092, Zürich, Switzerland
106 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...