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Studies on several problems on infinitely divisible processes and infinitely divisible distributions

Research Project

Project/Area Number 19340025
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKeio University

Principal Investigator

MAEJIMA Makoto  Keio University, 理工学部, 教授 (90051846)

Co-Investigator(Kenkyū-buntansha) NAKADA Hitoshi  慶應義塾大学, 理工学部, 教授 (40118980)
TAMURA Yozo  慶應義塾大学, 理工学部, 准教授 (50171905)
YASUDA Kumi  慶應義塾大学, 商学部, 准教授 (40284484)
SUZUKI Yuki  慶應義塾大学, 医学部, 講師 (30286645)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2008: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2007: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Keywords無限分解可能過程 / 無限分解可能分布 / レヴィ過程 / レヴィ測度 / オルンシュタイン・ウーレンベック過程 / α-自己分解可能分布 / 国際研究者交流 / スイス:メキシコ:フランス / フラクショナルレヴィ過程 / 自由確率論 / メキシコ、シンガポール / メキシコ:台湾
Research Abstract

Subclasses of infinitely divisible distributions are characterized as ranges of stochastic integral mappings with respect to Levy processes. There was a conjecture that the limiting classes obtained by the iteration of such mappings are identical to the closure of the class of stable distributions for many mappings. We succeeded to show that the conjecture is true. Further, we solved one problem unsolved for long time that is a characterization of semi-selfdecomposable distribution by a stochastic integral mapping with Levy processes. In addition to those, we solved many related problems and found many new ideas for the further studies.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (61 results)

All 2010 2009 2008 2007 Other

All Journal Article (40 results) (of which Peer Reviewed: 22 results) Presentation (18 results) Remarks (3 results)

  • [Journal Article] On the Lenstra constant associated to the Rosen continued fractions2010

    • Author(s)
      Hitoshi Nakada
    • Journal Title

      J.Eur.Math.Soc. 12

      Pages: 55-70

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Brjuno functions associated to α-continued fractions2010

    • Author(s)
      Laura Luzzi
    • Journal Title

      J.Approx.Theory 162

      Pages: 24-41

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov processes on R^2 with ultrametric jumps2010

    • Author(s)
      Kumi Yasuda
    • Journal Title

      京都大学数理解析研究所講究録 1672

      Pages: 111-116

    • Related Report
      2009 Annual Research Report
  • [Journal Article] A note on new classes of infinitely divisible distributions on R^d, Electr.2009

    • Author(s)
      M. Maejima, G. Nakahara
    • Journal Title

      Commun. Probab 14

      Pages: 358-371

    • Related Report
      2009 Final Research Report
  • [Journal Article] Stochastic integral characterizations of semi-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes, Commun.2009

    • Author(s)
      M. Maejima, Y. Ueda
    • Journal Title

      Stoch. Anal 3

      Pages: 349-367

    • Related Report
      2009 Final Research Report
  • [Journal Article] The limits of nested subclasses of several classes of infinitely divisible distributions are identical to the closure of the class of stable distributions2009

    • Author(s)
      M. Maejima, K. Sato
    • Journal Title

      Probab. Th. Rel. Fields 145

      Pages: 119-142

    • Related Report
      2009 Final Research Report
  • [Journal Article] Metric and arithmetic properties of mediant-Rosen maps.2009

    • Author(s)
      C. Kraaikamp, H. Nakada, T. Schmidt
    • Journal Title

      Acta Arith 137

      Pages: 295-324

    • Related Report
      2009 Final Research Report
  • [Journal Article] The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions2009

    • Author(s)
      Makoto Maejima
    • Journal Title

      Probab.Th.Relat.Fields 145

      Pages: 119-142

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on new classes of infinitely divisible distributions on R^d2009

    • Author(s)
      Makoto Maejima
    • Journal Title

      Electr.Commun.Probab. 14

      Pages: 358-371

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic integral characterizations of semi-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes2009

    • Author(s)
      Makoto Maejima
    • Journal Title

      Commun.Stoch.Anal. 3

      Pages: 349-367

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The limits of nested subclasses of several classes of infinitely divisible distributions are identical to the closure of the class of stable distributions2009

    • Author(s)
      Makoto Maejima
    • Journal Title

      Probability Theory and Related Fields 掲載決定

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov processes on the adeles2009

    • Author(s)
      Kumi Yasuda
    • Journal Title

      Journal of Theoretical Probability 掲載決定

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large deviation for stochastic line integrals as L^p-currents2009

    • Author(s)
      Shigeo Kusuoka
    • Journal Title

      Probability Theory and Related Fields 掲載決定

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limit theorems for weighted sums of infinite variance random variables attracted to integrals of linear fractional stable motions2008

    • Author(s)
      M. Maejima, S. Suzuki
    • Journal Title

      Tokyo J. Math. 31

      Pages: 259-271

    • Related Report
      2009 Final Research Report
  • [Journal Article] A subclass of type G selfdecomposable distributions on R^d2008

    • Author(s)
      T. Aoyama, M. Maejima, J. Rosinski
    • Journal Title

      J. Theoret. Probab. 21

      Pages: 14-34

    • Related Report
      2009 Final Research Report
  • [Journal Article] Limits of bifractional Brownian noises2008

    • Author(s)
      M. Maejima, C.A. Tudor
    • Journal Title

      Comm. Stoch. Anal. 2

      Pages: 369-383

    • Related Report
      2009 Final Research Report
  • [Journal Article] Semigroups of Upsilon transformations2008

    • Author(s)
      O.E. Barhdorff-Nielsen, M, Maejima
    • Journal Title

      Stoch. Proc. Appl. 118

      Pages: 2334-2343

    • Related Report
      2009 Final Research Report
  • [Journal Article] The non-monotonicity of the entropy ofα-continued fraction transformations2008

    • Author(s)
      H. Nakada
    • Journal Title

      Nonlinearity 21

      Pages: 1207-1225

    • Related Report
      2009 Final Research Report
  • [Journal Article] Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators2008

    • Author(s)
      V. Berthe, H. Nakada
    • Journal Title

      Finite Fields Appl 14

      Pages: 849-866

    • Related Report
      2009 Final Research Report
  • [Journal Article] A diffusion process with a random potential consisting of two self-similar processes with different indices2008

    • Author(s)
      Y. Suzuki
    • Journal Title

      Tokyo J. Math 31

      Pages: 511-532

    • Related Report
      2009 Final Research Report
  • [Journal Article] A subclass of type G selfdecomposable distributions on K^d2008

    • Author(s)
      Takahiro Aoyama
    • Journal Title

      Journal of Theoretical Probability 21

      Pages: 14-34

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limits of bifractional Brownian noises2008

    • Author(s)
      Makoto Maejima
    • Journal Title

      Communications on Stochastic Analysis 2(掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limit theorems for weighted sums of infinite variance random variables attracted to integrals of linear fractional stable motions2008

    • Author(s)
      Makoto Maejima
    • Journal Title

      Tokyo Journal of Mathematics 31

      Pages: 259-271

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The non-monotonicity of the entropy of α-continued fraction transformations2008

    • Author(s)
      Hitoshi Nakada
    • Journal Title

      Nonlinearity 21

      Pages: 1207-1225

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators2008

    • Author(s)
      Velerie Berthe
    • Journal Title

      Finite Fields and their applications 14

      Pages: 849-866

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A diffusion process with a random potential consisting of two self-similar processes with different indices2008

    • Author(s)
      Yuki Suzuki
    • Journal Title

      Tokyo Journal of Mathematics 31

      Pages: 511-532

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semigroups of Upsilon transformations2008

    • Author(s)
      O. E. Barhdorff-Nielsen and M. Maejima
    • Journal Title

      Stochastic Processes and Their Applications (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Subclass of Goldie-Steutel-Bondeson class of infinitely divisible distributions on R^d by Upsilon-mapping2007

    • Author(s)
      M. Maejima
    • Journal Title

      ALEA 3

      Pages: 50-66

    • Related Report
      2009 Final Research Report
  • [Journal Article] Operator-semistable, operator semi-selfdecomposable probability measures and related nested classes on p-adic vector spaces2007

    • Author(s)
      M. Maejima, R. Shah
    • Journal Title

      Monatschefte fur Matheamtik 151

      Pages: 293-318

    • Related Report
      2009 Final Research Report
  • [Journal Article] Wiener integrals with respect to the Hermite Processes and a non-central limit theorem2007

    • Author(s)
      M. Maejima, C.A. Tudor
    • Journal Title

      Stoch. Anal. Appl 25

      Pages: 1043-1056

    • Related Report
      2009 Final Research Report
  • [Journal Article] Exchangeable, Gibbs and equilibrium measures for Markov subshifts2007

    • Author(s)
      J. Aaronson, H. Nakada
    • Journal Title

      Ergodic Th. Dynamical Systems 27

      Pages: 535-545

    • Related Report
      2009 Final Research Report
  • [Journal Article] Invariance principles for Diophantine approximation of formal Laurent series over a finite base field2007

    • Author(s)
      E. Deligero, M. Fuchs, H. Nakada
    • Journal Title

      Finite Fields Appl 13

      Pages: 535-545

    • Related Report
      2009 Final Research Report
  • [Journal Article] On a formula on the potential operators of absorbing Levy processes in the half space2007

    • Author(s)
      Y. Tamura, H. Tanaka
    • Journal Title

      Stoch. Proc. Appl 118

      Pages: 199-212

    • Related Report
      2009 Final Research Report
  • [Journal Article] Subclass of Goldie-Steutel-Bondesson class of infinitely divisible distributions on R^d by Upsilon-mapping2007

    • Author(s)
      M. Maejima
    • Journal Title

      ALEA 3

      Pages: 50-66

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Operator-semistable,operator semi-selfdecomposable probability measures and related nested classes on p-adic vector spaces2007

    • Author(s)
      M. Maejima and R. Shah
    • Journal Title

      Monatschefte fur Matheamtik 151

      Pages: 293-318

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wiener integrals with respect to the Hermite Processes and a non-central limit theorem2007

    • Author(s)
      M. Maejima and C. A.Tudor
    • Journal Title

      Stochastic Analysis and Applications 25

      Pages: 1043-1056

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exchangeable, Gibbs and equilibrium measures for Markov subshifts2007

    • Author(s)
      J. Aaronson and H. Nakada
    • Journal Title

      Ergodic Theory and Dynamical Systems 27

      Pages: 535-545

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Invariance principles for Diophantine approximation of formal Laurent series over a finite base field2007

    • Author(s)
      E. Deligero, M. Fuchs and H. Nakada
    • Journal Title

      Finite Fields and Their Applications 13

      Pages: 535-545

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some ergodic properties of the negative slope algorithm2007

    • Author(s)
      K. Ishimura and H. Nakada
    • Journal Title

      Osaka Journal of Mathematics 44

      Pages: 667-683

    • NAID

      120005986765

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a formula on the potential operators of absorbing Levy processes in the half space2007

    • Author(s)
      Y. Tamura and H. Tanaka
    • Journal Title

      Stochastic Processes and Their Applications 118

      Pages: 199-212

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] A new family of mappings of infinitelydivisible distributions related to the Goldie-Steutel-Bondesson class2010

    • Author(s)
      青山崇洋, A. Lindner, 前島信
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-25
    • Related Report
      2009 Final Research Report
  • [Presentation] A new family of mappings of infinitely divisible distributions related to the Goldie-Steutel-Bondesson class2010

    • Author(s)
      青山崇洋
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶應義塾大学理工学部
    • Year and Date
      2010-03-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Entropy of a class of continued fraction maps2009

    • Author(s)
      H. Nakada
    • Organizer
      UK-Japan Winter School
    • Place of Presentation
      英国バース大学
    • Year and Date
      2009-01-10
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] 無限分解可能分布のサブクラスの極限について2008

    • Author(s)
      前島信
    • Organizer
      日本数学会2008年度秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] Fully subtractive algorithmのdynamicsについて2008

    • Author(s)
      仲田均
    • Organizer
      Dynamics of complex systems 2008-数学的予測方式の可能性と諸分野からのニーズ-
    • Place of Presentation
      北海道大学
    • Year and Date
      2008-09-03
    • Related Report
      2009 Final Research Report
  • [Presentation] Fully subtractive algorithm のdynamicsについて2008

    • Author(s)
      仲田 均
    • Organizer
      Dynamics of complex systems 2008 --数学的予測方式の可能性と諸分野からのニーズ--
    • Place of Presentation
      北海道大学
    • Year and Date
      2008-09-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] The limits of nested subclasses of several classes of infinitely divisible distributions2008

    • Author(s)
      M. Maejima
    • Organizer
      7th World Congress in Probability and Statistics
    • Place of Presentation
      Singapore
    • Year and Date
      2008-07-16
    • Related Report
      2009 Final Research Report
  • [Presentation] The limits of nested subclasses of several classes of infinitely divisible distributions2008

    • Author(s)
      Makoto Maejima
    • Organizer
      7^<th> World Congress in Probability and Statis tics
    • Place of Presentation
      シンガポール
    • Year and Date
      2008-07-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the metric Diophantine approximations in positive characteristic2007

    • Author(s)
      H. Nakada
    • Organizer
      Journee corps finis at LIRMM
    • Place of Presentation
      Montpellier, France
    • Year and Date
      2007-11-28
    • Related Report
      2009 Final Research Report
  • [Presentation] On the metric Diophantine approximations in positive characteristic2007

    • Author(s)
      H.Nakada
    • Organizer
      Journee corps finis at LIEMM
    • Place of Presentation
      Montpellier,France
    • Year and Date
      2007-11-28
    • Related Report
      2007 Annual Research Report
  • [Presentation] α-連分数変換から作られる確率過程の1-parameter familyのentropyの変化について2007

    • Author(s)
      仲田均, 夏井理恵
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2009 Final Research Report
  • [Presentation] α-連分数変換から作られる確率過程の1-parameter family のentropyの変化について2007

    • Author(s)
      H. Nakada(with Rie Natsui)
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] To which class do known real valued infinitely divisible distributions belong to?2007

    • Author(s)
      M. Maejima
    • Organizer
      5th International Conference on Levy Processes andApplications
    • Place of Presentation
      Copenhagen, Denmark
    • Year and Date
      2007-08-16
    • Related Report
      2009 Final Research Report
  • [Presentation] To which class do known real valued infinitely divisible distributions belong to?2007

    • Author(s)
      M. Maejima
    • Organizer
      5^<th> International Conference on Levy Processes and Applications
    • Place of Presentation
      Copenhagen,Denmark
    • Year and Date
      2007-08-16
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the non-monotonicityof the entropy of alpha-continued fraction transformations2007

    • Author(s)
      H. Nakada
    • Organizer
      Workshop on Dynamical systems and Number Theory 2007
    • Place of Presentation
      Strobl, Austria
    • Year and Date
      2007-07-02
    • Related Report
      2009 Final Research Report
  • [Presentation] On the non-monotonicity of the entropy of alpha-continued fraction transformations2007

    • Author(s)
      H. Nakada
    • Organizer
      Workshop on Dynamical Systems and NumberTheory 2007
    • Place of Presentation
      Strobl,Austria
    • Year and Date
      2007-07-02
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the Lenstra constantassociated to continued fractions2007

    • Author(s)
      H. Nakada
    • Organizer
      Workshop at Special Trimester on Dynamical Systems and Number Theory
    • Place of Presentation
      Scuola Normale Superiore at Pisa, Italy.
    • Year and Date
      2007-04-26
    • Related Report
      2009 Final Research Report
  • [Presentation] On the Lenstra constant associated to continued fractions2007

    • Author(s)
      H. Nakada
    • Organizer
      Workshop at Special Trimester on Dynamical Systems and Number Theory
    • Place of Presentation
      Scuola Normale Superiore at Pisa,Italy
    • Year and Date
      2007-04-26
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.keio.ac.jp/~maejima/

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.keio.ac.jp/local/maejima/

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.keio.ac.jp/local/maejima/

    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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