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Basic Research for a Singular Class of Measure-Valued Stochastic Processes and Associated Nonlinear Systems.

Research Project

Project/Area Number 14540101
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 InstitutionSAITAMA UNIVERSITY

Principal Investigator

DOKU Isamu  SAITAMA UNIVERSITY, Faculty of Education, Professor, 教育学部, 教授 (60207686)

Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
KeywordsMeasure-valued stochastic processes / Branching processes / Random measures / Interactive particle systems / Immigration superprocesses / Scaling / Limit theorem / Convergence problem / 測定値確率過程 / ランダム測定 / 超ブラウン運動 / 確率偏微分方程式 / 法則の絶対連続性 / 測度値過程 / 分枝マルコフ過程 / 特異分枝率 / 非線形方程式 / 許容的加法的汎関数 / 超過程 / 速度値過程 / 特異分岐率
Research Abstract

Our main interest is a class of singular superprocesses. First of all we proved that there exists a unique measure-valued branching Markov process for a wider class of singular branching rates, which includes a Fleischmann-Muller superprocess with hyperbolic branching rate. We also showed the regularity of their paths. Then we derived a sufficient condition for such a class of superprocesses to possess the finite time extinction property. Moreover, we extended those results to a class of generalized superprocesses with diffusion-like spatial motion.
Next we tried to obtain a generalization of Dawson-Li-Zhon convergence result to SCSM. Actually we considered a more complicated class of superprocesses with immigration, and proved a limit theorem that rescaled immigration superprocesses converges to a SCSM in the sense of distribution on the space of measure-valued continuous paths. Now we are planning a new research project that we aim at deriving a new type of limit theorem, where a superprocess more generalized than SCSM arises as a rescaled limit.
Furthermore, we proved an existence and uniqueness theorem for weak solution to various kinds of stochastic equations associated with such a class of singular superprocesses. For a specific example, we showed absolute continuity of the law of solution by applying stochastic analysis.

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (42 results)

All 2006 2005 2004 2003 2002 Other

All Journal Article (31 results) Book (2 results) Publications (9 results)

  • [Journal Article] A system of stochastic partial differential equations driven by a coloured noise and the martingale problem for symbiotic branching superprocesses.2006

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.55,no.1

      Pages: 1-15

    • NAID

      40007330794

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A system of stochastic partial differential equations driven by a coloured noise and the martingale problem for symbiotic branching superprocesses.2006

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 55(1)

      Pages: 1-15

    • NAID

      40007330794

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A system of stochastic partial differential equations driven by a coloured noise and the martingale problem for symbiotic branching superprocesses.2006

    • Author(s)
      Isamu DOKU
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.& Nat.Sci.) Vol.55, No.1

      Pages: 1-15

    • NAID

      40007330794

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Absolute continuity of the law of the weak solution for jump-type SPDEs.2005

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.54,no.1

      Pages: 1-17

    • NAID

      40007330781

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A class of rescaled immigration superprocesses convergent to SCSM.2005

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.54,no.2

      Pages: 1-13

    • NAID

      40007330791

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Absolute continuity of the law of the weak solution for jump-type SPDEs.2005

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 54(1)

      Pages: 1-17

    • NAID

      40007330781

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A class of rescaled immigration superprocesses convergent to SCSM.2005

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 54(2)

      Pages: 1-13

    • NAID

      40007330791

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Absolute continuity of the law of the weak solution for jump-type SPDEs.2005

    • Author(s)
      Isamu DOKU
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.& Net.Sci.) Vol.54, No.1

      Pages: 1-17

    • NAID

      40007330781

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A class of rescaled immigration superprocesses convergent to SCSM.2005

    • Author(s)
      Isamu DOKU
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.& Nat.Sci.) Vol.54, No.2

      Pages: 1-13

    • NAID

      40007330791

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Absolute continuity of the law of the weak solution for jump-type SPDES.2005

    • Author(s)
      Isamu DOKU
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) Vol.54, No.1

      Pages: 1-17

    • NAID

      40007330781

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Mutually interactive type of measure-valued processes and approximation scheme.2004

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.53,no.1

      Pages: 5-20

    • NAID

      40006474838

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Interacting particle systems convergent to super-Brownian motion with locally infinite branching mass.2004

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.53,no.2

      Pages: 1-16

    • NAID

      40006474849

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Mutually interactive type of measure-valued processes and approximation scheme.2004

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 53(1)

      Pages: 5-20

    • NAID

      40006474838

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Mathematical Basis on Branching Random Systems. (in Japanese)2004

    • Author(s)
      Doku, I.
    • Journal Title

      Saitama Univ., Saitama

      Pages: 73-73

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Interacting particle systems convergent to super-Brownian motion with locally infinite branching mass.2004

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 53(2)

      Pages: 1-16

    • NAID

      40006474849

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Mutually interactive type of measure-valued processes and approximation scheme.2004

    • Author(s)
      Isamu DOKU
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) Vol.53, No.1

      Pages: 5-20

    • NAID

      40006474838

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Interacting particle systems convergent to super-Brownian motion with locally infinite branching mass.2004

    • Author(s)
      Isamu DOKU
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) Vol.53, No.2

      Pages: 1-16

    • NAID

      40006474849

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Measure valued Markov processes associated with weighted branching rate functional.2003

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.52,no.1

      Pages: 22-31

    • NAID

      40005964121

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Weighted additive functionals and a class of measure-valued Markov processes with singular branching rate.2003

    • Author(s)
      Isamu Doku
    • Journal Title

      Far East J.Theo.Stat. vol.9

      Pages: 1-80

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the construction of superdiffusions with singular branching rate via regularized approximation.2003

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.52,no.2

      Pages: 1-11

    • NAID

      40005964127

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Some nonlinear elliptic boundary value problems and killing property for singular superprocesses.2003

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.52,no.2

      Pages: 13-17

    • NAID

      40005964128

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Measure valued Markov processes associated with weighted branching rate functional.2003

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 52(1)

      Pages: 22-31

    • NAID

      40005964121

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Weighted additive functionals and a class of measure-valued Markov processes with singular branching rate.2003

    • Author(s)
      Doku, I.
    • Journal Title

      Far East J.Theo.Stat. 9

      Pages: 1-80

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the construction of superdiffusions with singular branching rate via regularized approximation.2003

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 52(2)

      Pages: 1-11

    • NAID

      40005964127

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Some nonlinear elliptic boundary value problems and killing property for singular superprocesses.2003

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 52(2)

      Pages: 13-17

    • NAID

      40005964128

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Historical approach to the support problem for measure-valued processes associated with nonlinear stochostic equations.2002

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.51,no.1

      Pages: 1-12

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] White noise approach to limit theorems for solutions of some Wick type nonlinear equations.2002

    • Author(s)
      Isamu Doku
    • Journal Title

      Far East J. Math. Sci. vol.4

      Pages: 137-187

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Compacite etroite des lois relatives a la densite de processes suggeree par un probleme de martingale.2002

    • Author(s)
      Isamu Doku
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) vol.51,no.2

      Pages: 1-15

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Historical approach to the support problem for measure-valued processes associated with nonlinear stochastic equations.2002

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 51(1)

      Pages: 1-12

    • NAID

      40005611214

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] White noise approach to limit theorems for solutions of some Wick type nonlinear equations.2002

    • Author(s)
      Doku, I.
    • Journal Title

      Far East J.Math.Sci. 4

      Pages: 137-187

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Compacite etroite des lois relatives a la densite de processus suggeree par un probleme de martingale.2002

    • Author(s)
      Doku, I.
    • Journal Title

      J.Saitama Univ.Fac.Educ.(Math.Nat.Sci.) 51(2)

      Pages: 1-15

    • NAID

      40005611221

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] 分枝ランダム系の基礎(半線形偏微分方程式の境界値問題との交流)2004

    • Author(s)
      道工 勇
    • Publisher
      埼玉大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] 「分枝ランダム系の基礎」半線形偏微分方程式の境界値問題との交流2004

    • Author(s)
      道工 勇
    • Publisher
      埼玉大学
    • Related Report
      2004 Annual Research Report
  • [Publications] Isamu DOKU: "Measure valued Markov processes associated with weighted branching rate functional"J.Saitama Univ.Math.Nat.Sci.. 52・1. 22-31 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Isamu DOKU: "Weighted additive functionals and a class of measure-valued Markov processes with singular branching rate"Far East J.Theo.Stat.(FJTS). 9・1. 1-80 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Isamu DOKU: "On the construction of superdiffusions with singular branching rate via regularized approximation"J.Saitama Univ.Math.Nat.Sci.. 52・2. 1-11 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Isamu DOKU: "Some nonlinear elliptic boundary value problems and killing property for singular superprocesses"J.Saitama Univ.Math.Nat.Sci.. 52・2. 13-17 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Isamu DOKU: "Mutually interactive type of measure-valued processes and approximation scheme"J.Saitama Univ.Math.Nat.Sci. I. 53・1. 5-20 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Isamu DOKU: "Historical Approach to the support problem for measure-valued processes associated with nonlinear stochastic equations"J. Saitama Univ. Math. Nat. Sci.. 51・1. 1-12 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Isamu DOKU: "White noise approach to limit theorems for solutions of some Wick type nonlinear equations"Far East J. Math. Sci.. 4・2. 137-187 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Isamu DOKU: "Compacite etroite des lois relatives a la densite de processus suggeree par un probleme de martingale"J. Saitama Univ. Math. Nat. Sci.. 51・2. 1-15 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Isamu DOKU: "Measure valued Markov processes associated with weighted branching rate functional"J. Saitama Univ. Math. Nat. Sci.. 52・1. 1-9 (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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