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Genealogy of Fleming-Viot processes

Research Project

Project/Area Number 08640260
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya City University (1997)
Yokohama National University (1996)

Principal Investigator

SHIMIZU Akinobu  Nagoya City University, Institute of Natural Sciences, Professor, 自然科学研究教育センター, 教授 (10015547)

Co-Investigator(Kenkyū-buntansha) HASHIMOTO Yoshiaki  Nagoya City University, Institute of Natural Sciences.Professor, 自然科学研究教育センター, 教授 (50106259)
OKUTO Yuji  Nagoya City University, Institute of Natural Sciences, Professor, 自然科学研究教育センター, 教授 (80295625)
MISAWA Tetsuya  Nagoya City University, Faculty of Economics, Associate Professor, 経済学部, 助教授 (10190620)
MIYAHARA Yoshio  Nagoya City University, Faculty of Economics, Professor, 経済学部, 教授 (20106256)
KONNO Norio  Yokohama National University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (80205575)
寺田 敏司  横浜国立大学, 工学部, 教授 (80126383)
平野 載倫  横浜国立大学, 工学部, 教授 (80134815)
玉野 研一  横浜国立大学, 工学部, 教授 (90171892)
北田 泰彦  横浜国立大学, 工学部, 教授 (70016145)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1997: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1996: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordsmeasure-valued diffusion / infinite site model / stepping stone model / genealogy / infinite allele model / population genetics / 系図過程 / フレミング-ヴィオ過程 / 無限アリルモデル / 集団道伝学 / 対立遺伝子数 / 確率論
Research Abstract

The head investigator has investigated a genealogical problem of a stepping stone Fleming-Viot process. He got the following results : The average probability that two genes randomly chosen in the stationary state of the diffusion have a common ancestor is written in the term of the coalescent time of the dual process. Assume that the set of colonies is the d-dimensional lattice, and that the migration process is a random walk. Then, in order that the two genes have a common ancestor with probability 1, it is necessary and sufficient that the dimension d is less than or equal to 2. The average probability that the number of all mutations since the common anscestor equals s is given by a mixture of Poisson distributions.
Next, the head investigator has investigated the number of alleles in a sample of finite genes for stepping stone models with infinitely many alleles. His motivation is to try to extend the well-known results in the case without geographical structure for stepping stone models. This is a joint work with T.Soshi.
The investigator, N.Konno, has investigated infinite particle systems. He got many results in mathematical aspects and applied fields. The investigator, Y.Miyahara has investigated canonical martingale measures related to incomplete assets markets. The investigator, T.Misawa, has investigated stochastic dynamical systems. He got conserved quantities observing symmetry of dynamical systems.

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (43 results)

All Other

All Publications (43 results)

  • [Publications] A.Shimizu: "A genealogical problem of a stepping stone Fleming-Viot process," to appear in Annual Review,Nagoya City Univ.,Institute of Natural Sciences. Voi.2. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Konno: "Bounds on the critical value for the one-sided contact process," Proceedings of International Workshop on Soft Computing in Industry ´96. 72-77 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Yu.Tretyakov et al.,: "Numerical estimations of the critical value for the one-sided contact process" Proceedings of International Workshop on Soft Computing in Industry ´96. 84-89 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Sato et al.,: "Diffusive generalized contact processes and their coalescing dualities," Proceedings of International Workshop on Soft Computing in Industry ´96. 89-93 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] V.Belitsky et al.,: "A strong correlation inequality for contact processes and oriented percolation" Stochastic Processes and their Applications. Vol.67. 213-225 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Konno: "Upper bounds on survival probabilities for a nonattractive model," Journal of the Physical Society of Japan. Vol.66. 3751-3755 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Yu.Tretyakov et al.,: "Phase transtion for the one-sided contact prosess," Journal of the Physical Society of Japan. Vol.66. 3764-3769 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Sato et al: "Paper-scissors-stone game on trees" Memoirs of the Muroran Institute of Technology. Vol.47. 109-114 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Nakamura et al.,: "Upper bounds on percolation probabities for oriented bond percolation" Memoirs of the Muroran Institute of Technology. Vol.47. 115-121 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Konno: "Correlation inequalities and particle systems" Proceedings of Percolation Theory and Particle systems ´96. 89-111 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Inui et al.,: "Local directed percolation probability in two dimensions" Journal of the Physical Society of Japan. Vol.67. 99-102 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Miyahara: "Canonical martingale measures of jump type price processes in incomplete assets markets" Discussion Papers in Economics No.221,Faculty of Economics,Nagoya City Univ. (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Misawa: "The similarity method in stochastic dynamical systems" IMA J Appl.Math. Vol.59. 261-272 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Misawa: "A method for deriving conserved quantities from the symmetry of stochastic dynamical systems" to appear in Nuovo Cimento. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Asada et al.,: "Nonlinear business cycle model in an open economy:noise effects on the drnamics" Proceedings of 1997 International Symposium on Nonlinear Theory and its Applications,Honolulu,USA. 505-507 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Shimizu: "A genealogical problem of a stepping stone Fleming-Viot process, to appear in Annual Review" Nagoya City Univ., Institute of Natural Sciences. Vol.2. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.konno: "Bounds on the critical value for the one-sided contact process" Proceedings of International Workshop on Soft Computing in Industry '96. 72-77 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Yu.Tretyakov et al.: "Numerical estimations of the critical value for the one-sided contact process" Proceedings of International Workshop on Soft Computing in Industry '96. 84-89 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Sato et al.: "Diffusive generalized contact processes and their coalescing dualities" Proceedings of International Workshop on Soft Computing in Industry '96. 89-93 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] V.Belitsky et al.: "A strong correlation inequality for contact processes and oriented percolation" Stochastic Processes and their Applications. Vol.67. 213-225 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Konno: "Upper bounds on survival probabilities for a nonattractive model" Journal of the Physical Society of Japan. Vol.66. 3751-3755 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Yu.Tretyakov et al.: "Phase transition for the one-sided contact process" Journal of the Physical Society of Japan. Vol.66. 3764-3769 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Sato et al.: "Paper-scissors-stone game on trees" Memoirs of the Muroran Institute of Technology. Vol.47. 109-114 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Nakamura et al.: "Upper bounds on percolation probabilities for oriented bond percolation" Memoirs of the Muroran Institute of Technology. Vol.47. 115-121 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Konno: "Correlation inequalities and particle systems" Proceedings of Percolation Theory and Particle systems '96. 89-111 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Inui et al.: "Local directed percolation probability in two dimensions" Journal of the Physical Society of Japan. Vol.67. 99-102 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Miyahara: "Canonical martingale measures of jump type price processes in incomplete assets markets" Discussion Papers in Economics No.221, Faculty of Economics, Nagoya City Univ. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Misawa: "The similarity method in stochastic dynamical systems" IMA J.Appl.Math.Vol.59. 261-272 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Misawa: "A method for deriving conserved quantities from the symmetry of stochastic dynamical systems in Nuovo Cimento" to appear. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] T.Asada et al.: "Nonlinear business cycle model in an open economy : noise effects on the dynamics" Proceedings of 1997 International Symposium on Nonlinear Theory and its Applications, Honolulu, USA. 505-507 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Shimizu: "A genealogical problem of a stepping stone Fleming-Viot process" Annual Review,Nagoya city Univ.,Institute of Natural Scicnes. 2. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] V.Belitsky: "A strong correlation inequality for contact processes and oriented percolation" Stochastic Processes and their Applications. 67. 213-225 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Konno: "Upper bounds on survival probabilities for a non attractive model" J.Phys.Soc.Japan. 66. 3751-3755 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Konno: "Correlation inequalities and particle systems" Proceedings of Percolation Theory and Particle systems '96. 89-111 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Misawa: "The similarity method in stochastic dynamical systems" IMA J.Appl.Math.59. 261-272 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Misawa: "A method for deriving conserved quantities from the symmetry of stoch dynamical systems" Nuovo Cimento. (to.appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Konno: "Bounds on critical value for the one-sided contact process" Proc.of Int.Workshop on Soft Computing Industry. 72-77 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Sato: "Diffusive generalized contact processes and their coalescin dualities" Proc.of Int.Workshop on Soft Computing Industry. 88-93 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] V.Belitsky: "A strong correlation inequality for contact processes and oriented percolation" Stochastic Processes and their Applications. (to appear). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] N.Saitok: "An analysis of a family of rational maps containing integrable and non-integrable diffrence analogue of the logistic equation" J.phys.A : Math.Gen.29. 1831-1840 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] O.Okunev: "Lindelof prowers and products of function spaces" Proc.American Math.Soc.Vol.124. 2905-2915 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] N.Hirano: "Multiplicity and stability result for semilinear parabolic equations" Discrete and Continuous Dynamical Systems. Vol.2. 271-280 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] N.Konno: "Lecture Notes on Harris Lemma and Particle Systems" Universidade de Sao Paulo, 87 (1996)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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