Karhunen-Loeve expansions for the m-th order detrended Brownian motion View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2014-10

AUTHORS

XiaoHui Ai, WenBo V. Li

ABSTRACT

The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve expansion for the process and establish a connection with the generalized (m-th order) Brownian bridge developed by MacNeill (1978) in the study of distributions of polynomial regression. The resulting distribution identity is also verified by a stochastic Fubini approach. As applications, large and small deviation asymptotic behaviors for the L2 norm are given. More... »

PAGES

2043-2052

References to SciGraph publications

  • 2011-02. Karhunen-Loève expansions of α-Wiener bridges in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
  • 1992-01. Comparison results for the lower tail of Gaussian seminorms in JOURNAL OF THEORETICAL PROBABILITY
  • 2005-07. Exact Small Ball Constants for Some Gaussian Processes under the L2-Norm in JOURNAL OF MATHEMATICAL SCIENCES
  • 1988-02. Cholesky decomposition of the Hilbert matrix in JAPAN JOURNAL OF APPLIED MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11425-014-4873-4

    DOI

    http://dx.doi.org/10.1007/s11425-014-4873-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046275878


    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/2008/0104", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Statistics", 
            "type": "DefinedTerm"
          }, 
          {
            "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"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Northeast Forestry University", 
              "id": "https://www.grid.ac/institutes/grid.412246.7", 
              "name": [
                "Department of Mathematics, Northeast Forestry University, 150040, Harbin, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ai", 
            "givenName": "XiaoHui", 
            "id": "sg:person.012160056551.17", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012160056551.17"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Delaware", 
              "id": "https://www.grid.ac/institutes/grid.33489.35", 
              "name": [
                "Department of Mathematical Sciences, University of Delaware, 19716, Newark, DE, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Li", 
            "givenName": "WenBo V.", 
            "id": "sg:person.014023162215.57", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014023162215.57"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/0304-4149(92)90123-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000426105"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0747-7171(08)80044-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006811531"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01046776", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017771201", 
              "https://doi.org/10.1007/bf01046776"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-07-04233-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025899876"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0378-3758(93)90107-h", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026691467"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.spl.2007.03.011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030965491"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf03167904", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035828668", 
              "https://doi.org/10.1007/bf03167904"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf03167904", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035828668", 
              "https://doi.org/10.1007/bf03167904"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10958-005-0197-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038010865", 
              "https://doi.org/10.1007/s10958-005-0197-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10958-005-0197-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038010865", 
              "https://doi.org/10.1007/s10958-005-0197-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.2478/s11533-010-0090-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040156559", 
              "https://doi.org/10.2478/s11533-010-0090-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.2478/s11533-010-0090-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040156559", 
              "https://doi.org/10.2478/s11533-010-0090-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.2478/s11533-010-0090-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040156559", 
              "https://doi.org/10.2478/s11533-010-0090-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.spl.2012.03.007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044854683"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.disc.2006.03.026", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045829078"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0894-0347-1990-1007910-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047906910"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/aos/1176344133", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064407399"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/2975779", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1070158154"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/074921706000000761", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1086780408"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2014-10", 
        "datePublishedReg": "2014-10-01", 
        "description": "The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve expansion for the process and establish a connection with the generalized (m-th order) Brownian bridge developed by MacNeill (1978) in the study of distributions of polynomial regression. The resulting distribution identity is also verified by a stochastic Fubini approach. As applications, large and small deviation asymptotic behaviors for the L2 norm are given.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s11425-014-4873-4", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1048022", 
            "issn": [
              "1674-7283", 
              "1869-1862"
            ], 
            "name": "Science China Mathematics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "10", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "57"
          }
        ], 
        "name": "Karhunen-Loeve expansions for the m-th order detrended Brownian motion", 
        "pagination": "2043-2052", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "dc6fb0cb4be3d04dc25cde2aec9fdb9ddf9c9ee30e60f87da217b90faee70427"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s11425-014-4873-4"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1046275878"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s11425-014-4873-4", 
          "https://app.dimensions.ai/details/publication/pub.1046275878"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T13:20", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8659_00000524.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs11425-014-4873-4"
      }
    ]
     

    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/s11425-014-4873-4'

    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/s11425-014-4873-4'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11425-014-4873-4'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11425-014-4873-4'


     

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

    120 TRIPLES      21 PREDICATES      42 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s11425-014-4873-4 schema:about anzsrc-for:01
    2 anzsrc-for:0104
    3 schema:author N71e93350933048f69ae21d46e285a336
    4 schema:citation sg:pub.10.1007/bf01046776
    5 sg:pub.10.1007/bf03167904
    6 sg:pub.10.1007/s10958-005-0197-9
    7 sg:pub.10.2478/s11533-010-0090-8
    8 https://doi.org/10.1016/0304-4149(92)90123-8
    9 https://doi.org/10.1016/0378-3758(93)90107-h
    10 https://doi.org/10.1016/j.disc.2006.03.026
    11 https://doi.org/10.1016/j.spl.2007.03.011
    12 https://doi.org/10.1016/j.spl.2012.03.007
    13 https://doi.org/10.1016/s0747-7171(08)80044-2
    14 https://doi.org/10.1090/s0002-9947-07-04233-x
    15 https://doi.org/10.1090/s0894-0347-1990-1007910-7
    16 https://doi.org/10.1214/074921706000000761
    17 https://doi.org/10.1214/aos/1176344133
    18 https://doi.org/10.2307/2975779
    19 schema:datePublished 2014-10
    20 schema:datePublishedReg 2014-10-01
    21 schema:description The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve expansion for the process and establish a connection with the generalized (m-th order) Brownian bridge developed by MacNeill (1978) in the study of distributions of polynomial regression. The resulting distribution identity is also verified by a stochastic Fubini approach. As applications, large and small deviation asymptotic behaviors for the L2 norm are given.
    22 schema:genre research_article
    23 schema:inLanguage en
    24 schema:isAccessibleForFree false
    25 schema:isPartOf N1a71e964e2ad4a10abaf0ace91f3e63d
    26 N8a26f40e38634a37a4e85028893cd45e
    27 sg:journal.1048022
    28 schema:name Karhunen-Loeve expansions for the m-th order detrended Brownian motion
    29 schema:pagination 2043-2052
    30 schema:productId N5c06d93d911347e09582a06ab68f2d82
    31 Na4038a0fbec84e80aac397fc3b69ff8b
    32 Ne38607a9dc6c4fbab9797c8b1fdeadf7
    33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046275878
    34 https://doi.org/10.1007/s11425-014-4873-4
    35 schema:sdDatePublished 2019-04-10T13:20
    36 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    37 schema:sdPublisher Nba52b21465e5418a92a0a40580b14a50
    38 schema:url http://link.springer.com/10.1007%2Fs11425-014-4873-4
    39 sgo:license sg:explorer/license/
    40 sgo:sdDataset articles
    41 rdf:type schema:ScholarlyArticle
    42 N1a71e964e2ad4a10abaf0ace91f3e63d schema:issueNumber 10
    43 rdf:type schema:PublicationIssue
    44 N5c06d93d911347e09582a06ab68f2d82 schema:name dimensions_id
    45 schema:value pub.1046275878
    46 rdf:type schema:PropertyValue
    47 N71e93350933048f69ae21d46e285a336 rdf:first sg:person.012160056551.17
    48 rdf:rest N828002327fa9418389ebb29c646b87e2
    49 N828002327fa9418389ebb29c646b87e2 rdf:first sg:person.014023162215.57
    50 rdf:rest rdf:nil
    51 N8a26f40e38634a37a4e85028893cd45e schema:volumeNumber 57
    52 rdf:type schema:PublicationVolume
    53 Na4038a0fbec84e80aac397fc3b69ff8b schema:name readcube_id
    54 schema:value dc6fb0cb4be3d04dc25cde2aec9fdb9ddf9c9ee30e60f87da217b90faee70427
    55 rdf:type schema:PropertyValue
    56 Nba52b21465e5418a92a0a40580b14a50 schema:name Springer Nature - SN SciGraph project
    57 rdf:type schema:Organization
    58 Ne38607a9dc6c4fbab9797c8b1fdeadf7 schema:name doi
    59 schema:value 10.1007/s11425-014-4873-4
    60 rdf:type schema:PropertyValue
    61 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    62 schema:name Mathematical Sciences
    63 rdf:type schema:DefinedTerm
    64 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
    65 schema:name Statistics
    66 rdf:type schema:DefinedTerm
    67 sg:journal.1048022 schema:issn 1674-7283
    68 1869-1862
    69 schema:name Science China Mathematics
    70 rdf:type schema:Periodical
    71 sg:person.012160056551.17 schema:affiliation https://www.grid.ac/institutes/grid.412246.7
    72 schema:familyName Ai
    73 schema:givenName XiaoHui
    74 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012160056551.17
    75 rdf:type schema:Person
    76 sg:person.014023162215.57 schema:affiliation https://www.grid.ac/institutes/grid.33489.35
    77 schema:familyName Li
    78 schema:givenName WenBo V.
    79 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014023162215.57
    80 rdf:type schema:Person
    81 sg:pub.10.1007/bf01046776 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017771201
    82 https://doi.org/10.1007/bf01046776
    83 rdf:type schema:CreativeWork
    84 sg:pub.10.1007/bf03167904 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035828668
    85 https://doi.org/10.1007/bf03167904
    86 rdf:type schema:CreativeWork
    87 sg:pub.10.1007/s10958-005-0197-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038010865
    88 https://doi.org/10.1007/s10958-005-0197-9
    89 rdf:type schema:CreativeWork
    90 sg:pub.10.2478/s11533-010-0090-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040156559
    91 https://doi.org/10.2478/s11533-010-0090-8
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1016/0304-4149(92)90123-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000426105
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1016/0378-3758(93)90107-h schema:sameAs https://app.dimensions.ai/details/publication/pub.1026691467
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1016/j.disc.2006.03.026 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045829078
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1016/j.spl.2007.03.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030965491
    100 rdf:type schema:CreativeWork
    101 https://doi.org/10.1016/j.spl.2012.03.007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044854683
    102 rdf:type schema:CreativeWork
    103 https://doi.org/10.1016/s0747-7171(08)80044-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006811531
    104 rdf:type schema:CreativeWork
    105 https://doi.org/10.1090/s0002-9947-07-04233-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1025899876
    106 rdf:type schema:CreativeWork
    107 https://doi.org/10.1090/s0894-0347-1990-1007910-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047906910
    108 rdf:type schema:CreativeWork
    109 https://doi.org/10.1214/074921706000000761 schema:sameAs https://app.dimensions.ai/details/publication/pub.1086780408
    110 rdf:type schema:CreativeWork
    111 https://doi.org/10.1214/aos/1176344133 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064407399
    112 rdf:type schema:CreativeWork
    113 https://doi.org/10.2307/2975779 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070158154
    114 rdf:type schema:CreativeWork
    115 https://www.grid.ac/institutes/grid.33489.35 schema:alternateName University of Delaware
    116 schema:name Department of Mathematical Sciences, University of Delaware, 19716, Newark, DE, USA
    117 rdf:type schema:Organization
    118 https://www.grid.ac/institutes/grid.412246.7 schema:alternateName Northeast Forestry University
    119 schema:name Department of Mathematics, Northeast Forestry University, 150040, Harbin, China
    120 rdf:type schema:Organization
     




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


    ...