Nonlinear Expectations and Stochastic Calculus under Uncertainty, with Robust CLT and G-Brownian Motion View Full Text


Ontology type: schema:Book      Open Access: True


Book Info

DATE

2019

GENRE

Monograph

AUTHORS

Shige Peng

PUBLISHER

Springer Nature

ABSTRACT

This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful. More... »

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-662-59903-7

DOI

http://dx.doi.org/10.1007/978-3-662-59903-7

ISBN

978-3-662-59902-0 | 978-3-662-59903-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1120936153


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"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Institute of Mathematics, Shandong University, Jinan, Shandong, China", 
          "id": "http://www.grid.ac/institutes/grid.27255.37", 
          "name": [
            "Institute of Mathematics, Shandong University, Jinan, Shandong, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Peng", 
        "givenName": "Shige", 
        "id": "sg:person.012375343637.10", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012375343637.10"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2019", 
    "datePublishedReg": "2019-01-01", 
    "description": "This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng\u2019s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.", 
    "genre": "monograph", 
    "id": "sg:pub.10.1007/978-3-662-59903-7", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isbn": [
      "978-3-662-59902-0", 
      "978-3-662-59903-7"
    ], 
    "keywords": [
      "nonlinear expectations", 
      "stochastic calculus", 
      "mathematical finance", 
      "probability theory", 
      "representation theorem", 
      "G-Brownian Motion", 
      "central limit theorem", 
      "lecture notes", 
      "integrable processes", 
      "sublinear expectations", 
      "stochastic analysis", 
      "G-expectation", 
      "limit theorem", 
      "Brownian motion", 
      "model uncertainty", 
      "graduate textbook", 
      "theorem", 
      "normal distribution", 
      "basic definitions", 
      "coherent measures", 
      "calculus", 
      "theory", 
      "series of lectures", 
      "motion", 
      "uncertainty", 
      "summer school", 
      "integrals", 
      "large number", 
      "further references", 
      "recent developments", 
      "problem", 
      "research topic", 
      "CLT", 
      "notion", 
      "law", 
      "note", 
      "recent research topics", 
      "distribution", 
      "finance", 
      "number", 
      "chapter", 
      "definition", 
      "results", 
      "expectations", 
      "book", 
      "relation", 
      "topic", 
      "textbooks", 
      "analysis", 
      "lectures", 
      "reference", 
      "series", 
      "process", 
      "authors", 
      "researchers", 
      "materials", 
      "measures", 
      "end", 
      "coverage", 
      "comments", 
      "development", 
      "students", 
      "University", 
      "exercise", 
      "history", 
      "risk", 
      "schools", 
      "example"
    ], 
    "name": "Nonlinear Expectations and Stochastic Calculus under Uncertainty, with Robust CLT and G-Brownian Motion", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1120936153"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-662-59903-7"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-662-59903-7", 
      "https://app.dimensions.ai/details/publication/pub.1120936153"
    ], 
    "sdDataset": "books", 
    "sdDatePublished": "2022-06-01T22:26", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220601/entities/gbq_results/book/book_24.jsonl", 
    "type": "Book", 
    "url": "https://doi.org/10.1007/978-3-662-59903-7"
  }
]
 

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.10.1007/978-3-662-59903-7'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-662-59903-7'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-662-59903-7'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-662-59903-7'


 

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

122 TRIPLES      21 PREDICATES      94 URIs      86 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-662-59903-7 schema:about anzsrc-for:01
2 anzsrc-for:0102
3 anzsrc-for:0104
4 schema:author N25e081a0bf824bd48cce6a2ec6553519
5 schema:datePublished 2019
6 schema:datePublishedReg 2019-01-01
7 schema:description This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.
8 schema:genre monograph
9 schema:inLanguage en
10 schema:isAccessibleForFree true
11 schema:isbn 978-3-662-59902-0
12 978-3-662-59903-7
13 schema:keywords Brownian motion
14 CLT
15 G-Brownian Motion
16 G-expectation
17 University
18 analysis
19 authors
20 basic definitions
21 book
22 calculus
23 central limit theorem
24 chapter
25 coherent measures
26 comments
27 coverage
28 definition
29 development
30 distribution
31 end
32 example
33 exercise
34 expectations
35 finance
36 further references
37 graduate textbook
38 history
39 integrable processes
40 integrals
41 large number
42 law
43 lecture notes
44 lectures
45 limit theorem
46 materials
47 mathematical finance
48 measures
49 model uncertainty
50 motion
51 nonlinear expectations
52 normal distribution
53 note
54 notion
55 number
56 probability theory
57 problem
58 process
59 recent developments
60 recent research topics
61 reference
62 relation
63 representation theorem
64 research topic
65 researchers
66 results
67 risk
68 schools
69 series
70 series of lectures
71 stochastic analysis
72 stochastic calculus
73 students
74 sublinear expectations
75 summer school
76 textbooks
77 theorem
78 theory
79 topic
80 uncertainty
81 schema:name Nonlinear Expectations and Stochastic Calculus under Uncertainty, with Robust CLT and G-Brownian Motion
82 schema:productId Na24a1a7bdd8b48698e087126c506a54c
83 Nabc2ae963c48414fac422dcadb2dae49
84 schema:publisher Na1d6c6128d3d4f7895269f962a7c4128
85 schema:sameAs https://app.dimensions.ai/details/publication/pub.1120936153
86 https://doi.org/10.1007/978-3-662-59903-7
87 schema:sdDatePublished 2022-06-01T22:26
88 schema:sdLicense https://scigraph.springernature.com/explorer/license/
89 schema:sdPublisher Nf044348da7af4b77ae53d21fb0a3ec0b
90 schema:url https://doi.org/10.1007/978-3-662-59903-7
91 sgo:license sg:explorer/license/
92 sgo:sdDataset books
93 rdf:type schema:Book
94 N25e081a0bf824bd48cce6a2ec6553519 rdf:first sg:person.012375343637.10
95 rdf:rest rdf:nil
96 Na1d6c6128d3d4f7895269f962a7c4128 schema:name Springer Nature
97 rdf:type schema:Organisation
98 Na24a1a7bdd8b48698e087126c506a54c schema:name dimensions_id
99 schema:value pub.1120936153
100 rdf:type schema:PropertyValue
101 Nabc2ae963c48414fac422dcadb2dae49 schema:name doi
102 schema:value 10.1007/978-3-662-59903-7
103 rdf:type schema:PropertyValue
104 Nf044348da7af4b77ae53d21fb0a3ec0b schema:name Springer Nature - SN SciGraph project
105 rdf:type schema:Organization
106 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
107 schema:name Mathematical Sciences
108 rdf:type schema:DefinedTerm
109 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
110 schema:name Applied Mathematics
111 rdf:type schema:DefinedTerm
112 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
113 schema:name Statistics
114 rdf:type schema:DefinedTerm
115 sg:person.012375343637.10 schema:affiliation grid-institutes:grid.27255.37
116 schema:familyName Peng
117 schema:givenName Shige
118 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012375343637.10
119 rdf:type schema:Person
120 grid-institutes:grid.27255.37 schema:alternateName Institute of Mathematics, Shandong University, Jinan, Shandong, China
121 schema:name Institute of Mathematics, Shandong University, Jinan, Shandong, China
122 rdf:type schema:Organization
 




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


...