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Analysis of variations for self-similar processes : a stochastic calculus approach

Author: Ciprian Tudor
Publisher: Cham : Springer, 2013.
Series: Probability and its applications (Springer-Verlag)
Edition/Format:  eBook : Document : EnglishView all editions and formats
Summary:
Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ciprian Tudor
ISBN: 9783319009360 3319009362 9781299857636 1299857639 3319009354 9783319009353
OCLC Number: 857431888
Description: 1 online resource (xi, 268 pages) : illustrations
Contents: Part I: Examples of Self-similar Processes. Fractional Brownian Motion and Related Processes --
Solutions to the Linear Stochastic Heat and Wave Equation --
Non-Gaussian Self-similar Processes --
Multiparameter Gaussian Processes --
Part II: Variations of Self-similar Processes: Central and Non-Central Limit Theorems. First and Second Order Quadratic Variations. Wavelet-Type Variations --
Hermite Variations for Self-similar Processes.
Series Title: Probability and its applications (Springer-Verlag)
Responsibility: Ciprian Tudor.

Abstract:

Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades.  Read more...

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"The author provides the general theory for different classes of self-similar processes with a complete treatment of limit theorems for their variations. ... The book is self-contained and suitable Read more...

 
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Primary Entity<\/h3>\n
<http:\/\/www.worldcat.org\/oclc\/857431888<\/a>> # Analysis of variations for self-similar processes : a stochastic calculus approach<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:CreativeWork<\/a>, schema:Book<\/a>, schema:MediaObject<\/a> ;\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"857431888<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/sz<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/mathematics_probability_&_statistics_general<\/a>> ; # MATHEMATICS--Probability & Statistics--General<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/519.23\/e23\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/id.worldcat.org\/fast\/1111938<\/a>> ; # Self-similar processes<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/probability_theory<\/a>> ; # probability theory<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/statistics<\/a>> ; # statistics<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/id.worldcat.org\/fast\/844140<\/a>> ; # Calculus of variations<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/waarschijnlijkheidstheorie<\/a>> ; # waarschijnlijkheidstheorie<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/mathematics_applied<\/a>> ; # MATHEMATICS--Applied<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/mathematics_general<\/a>> ; # Mathematics (General)<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/stochastische_processen<\/a>> ; # stochastische processen<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/mathematics<\/a>> ; # mathematics<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/wiskunde_algemeen<\/a>> ; # Wiskunde (algemeen)<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/wiskunde<\/a>> ; # wiskunde<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/statistiek<\/a>> ; # statistiek<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/stochastic_processes<\/a>> ; # stochastic processes<\/span>\n\u00A0\u00A0\u00A0\nschema:author<\/a> <http:\/\/viaf.org\/viaf\/189541583<\/a>> ; # Ciprian Tudor<\/span>\n\u00A0\u00A0\u00A0\nschema:bookFormat<\/a> schema:EBook<\/a> ;\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2013<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/1655016779<\/a>> ;\u00A0\u00A0\u00A0\nschema:genre<\/a> \"Electronic books<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isPartOf<\/a> <http:\/\/worldcat.org\/issn\/1431-7028<\/a>> ; # Probability and its applications (Springer-Verlag),<\/span>\n\u00A0\u00A0\u00A0\nschema:isSimilarTo<\/a> <http:\/\/worldcat.org\/entity\/work\/data\/1655016779#CreativeWork\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Analysis of variations for self-similar processes : a stochastic calculus approach<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"857431888<\/span>\" ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/doi.org\/10.1007\/978-3-319-00936-0<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.myilibrary.com?id=517014<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/link.springer.com\/book\/10.1007\/978-3-319-00936-0<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/search.ebscohost.com\/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=626002<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/site.ebrary.com\/id\/10743805<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/public.ebookcentral.proquest.com\/choice\/publicfullrecord.aspx?p=1398619<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/link.springer.com\/book\/10.1007\/978-3-319-00935-3<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/discover.gcu.ac.uk\/discovery\/openurl?institution=44GLCU_INST&vid=44GLCU_INST:44GLCU_VU2&?u.ignore_date_coverage=true&rft.mms_id=991002483390903836<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9781299857636<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9783319009360<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/dx.doi.org\/10.1007\/978-3-319-00936-0<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9783319009353<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/857431888<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Related Entities<\/h3>\n
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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/mathematics<\/a>> # mathematics<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"mathematics<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/mathematics_applied<\/a>> # MATHEMATICS--Applied<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"MATHEMATICS--Applied<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/mathematics_general<\/a>> # Mathematics (General)<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Mathematics (General)<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/mathematics_probability_&_statistics_general<\/a>> # MATHEMATICS--Probability & Statistics--General<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"MATHEMATICS--Probability & Statistics--General<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/probability_theory<\/a>> # probability theory<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"probability theory<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/statistics<\/a>> # statistics<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"statistics<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/statistiek<\/a>> # statistiek<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"statistiek<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/stochastic_processes<\/a>> # stochastic processes<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"stochastic processes<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/stochastische_processen<\/a>> # stochastische processen<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"stochastische processen<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/waarschijnlijkheidstheorie<\/a>> # waarschijnlijkheidstheorie<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"waarschijnlijkheidstheorie<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/wiskunde<\/a>> # wiskunde<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"wiskunde<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/1655016779#Topic\/wiskunde_algemeen<\/a>> # Wiskunde (algemeen)<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Wiskunde (algemeen)<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/sz<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"sz<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.worldcat.org\/fast\/1111938<\/a>> # Self-similar processes<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Self-similar processes<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.worldcat.org\/fast\/844140<\/a>> # Calculus of variations<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Calculus of variations<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/189541583<\/a>> # Ciprian Tudor<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1973<\/span>\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Tudor<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Ciprian<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Ciprian Tudor<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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<http:\/\/worldcat.org\/isbn\/9781299857636<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"1299857639<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9781299857636<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9783319009353<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"3319009354<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9783319009353<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9783319009360<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"3319009362<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9783319009360<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/issn\/1431-7028<\/a>> # Probability and its applications (Springer-Verlag),<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:PublicationSeries<\/a> ;\u00A0\u00A0\u00A0\nschema:hasPart<\/a> <http:\/\/www.worldcat.org\/oclc\/857431888<\/a>> ; # Analysis of variations for self-similar processes : a stochastic calculus approach<\/span>\n\u00A0\u00A0\u00A0\nschema:issn<\/a> \"1431-7028<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Probability and its applications (Springer-Verlag),<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Probability and Its Applications,<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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Content-negotiable representations<\/p>\n