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Generalizations of infinite dimensional Laplacians, construction methods of stochastic processes and developments in quantum information analysis

Research Project

Project/Area Number 21540151
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 InstitutionMeijo University

Principal Investigator

SAITO Kimiaki  名城大学, 理工学部, 教授 (90195983)

Co-Investigator(Renkei-kenkyūsha) MATSUZAWA Tadato  名城大学, 理工学部, 教授 (20022618)
ICHIHARA Kanji  名城大学, 理工学部, 教授 (00112293)
MIMACHI Yuko (HARA Yuko)  名城大学, 理工学部, 准教授 (00218629)
NISHI Kenjiro  名城大学, 理工学部, 講師 (30076616)
OBATA Nobuaki  東北大学, 大学院・情報科学研究科, 教授 (10169360)
HIBINO Yuji  佐賀大学, 理工学部, 准教授 (50253589)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords無限次元ラプラス作用素 / 無限次元確率過程 / 確率過程構成法 / 量子情報解析 / Exotic Laplacian / レヴィ・ラプラシアンの一般化 / ホワイトノイズの高階微分 / チェサロヒルベルト空間
Research Abstract

In this research, we considered a quantization and a new approach to a quantum information analysis by researching the infinite dimensional stochastic analysis jointly from major fields : probability theory, analysis, graph theory, number theory and computer science. Especially we succeeded in constructing the theory of higher order derivatives of white noise based on the stochastic analysis associated with exotic Laplacians defined by higher order Cesaro means of the second differentiation. It is a quite important progress and a creative point that a quantum information analysis in this direction can be constructed.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (24 results)

All 2012 2011 2010 2009

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (11 results)

  • [Journal Article] Infinite dimensional Laplacians associated with derivatives of white noise2012

    • Author(s)
      K.Saito
    • Journal Title

      QP-PQ Quantum Probability and White Noise Analysis

      Volume: (掲載予定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Improvement of Howard's policy iteration method for application to policies modeled by periodic Markov chains2011

    • Author(s)
      Y. Uchimura, K. Saito
    • Journal Title

      Far East Journal of Mathematical Sciences

      Volume: Vol.57 Pages: 113-132

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stationary Distributions of the Bernoulli Type Galton-Watson Branching Process with Immigration2011

    • Author(s)
      Y. Uchimura, K. Saito
    • Journal Title

      Communications on Stochastic Analysis

      Volume: Vol.5, No.3 Pages: 457-480

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A characterization of the geometric Brownian motion in terms of infinite dimensional Laplacians2011

    • Author(s)
      I. Kitagawa, K. Saito, A. H. Tsoi
    • Journal Title

      Random Operators and Stochastic Equations

      Volume: Vol.19 Pages: 91-103

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exotic Laplacians and derivatives of white noise2011

    • Author(s)
      L. Accardi, U. C. Ji, K. Saito
    • Journal Title

      Infinite Dim. Anal., Quantum Prob. and Related Topics

      Volume: Vol.14 Pages: 1-14

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] IMPROVEMENT OF HOWARD'S POLICY ITERATION METHOD FOR APPLICATION TO POLICIES MODELED BY PERIODIC, MARKOV CHAINS2011

    • Author(s)
      K.Saito (with Y.Uchimura)
    • Journal Title

      Far East Journal of Mathematical Sciences

      Volume: Vol.57 Pages: 113-132

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A stationary distribution of the Bernoulli type Galton-Watson branchingprocess with immigration2011

    • Author(s)
      K.Saito (with Y.Uchimura)
    • Journal Title

      Communications on stochastic Analysis

      Volume: Vol.5 Pages: 457-480

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exotic Laplacians and derivatives of white noise2011

    • Author(s)
      K.Saito (with L.Accardi, U.C.Ji,)
    • Journal Title

      Infinite Dimensional Analysis, Quantum Probability and Related Topics

      Volume: Vol.14 Pages: 1-14

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A stationary distribution of the Bernoulli type Galton-Watson branching process with immigration2011

    • Author(s)
      K.Saito (with Y.Uchimura)
    • Journal Title

      Communications on Stochastic Analysis

      Volume: Vol.5(掲載予定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Gauss-Poisson correspondence and the Levy Laplacian2009

    • Author(s)
      K. Saito
    • Journal Title

      Interdisciplinary Information Sciences

      Volume: Vol.15, No.3 Pages: 431-440

    • NAID

      120001943155

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exotic Laplacians and associated stochastic processes2009

    • Author(s)
      L. Accardi, U. C. Ji and K. Saito
    • Journal Title

      Infinite Dimensional Analysis, QuantumProbability and Related Topics

      Volume: Vol.12, No.1 Pages: 1-19

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exotic Laplacians and associated stochastic processes2009

    • Author(s)
      K.Saito(with L.Accardi, U.C.Ji,)
    • Journal Title

      Infinite Dim.Anal., Quantum Prob.and Related Topics Vol.12

      Pages: 1-19

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Gauss-Poisson correspondence and the Levy Laplacian2009

    • Author(s)
      K.Saito
    • Journal Title

      Interdisciplinary Information Sciences Vol.15

      Pages: 431-440

    • NAID

      120001943155

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Infinite dimensional Laplacians associated with derivatives of white noise2011

    • Author(s)
      K. Saito
    • Organizer
      32nd International Conference on Quantum Probability and Related Topics
    • Place of Presentation
      Levico Terme. Italy, Invited Talk
    • Year and Date
      2011-05-30
    • Related Report
      2011 Final Research Report
  • [Presentation] Infinite dimensional Laplacians associated with derivatives of white noise2011

    • Author(s)
      K.Saito
    • Organizer
      32nd INTERNATIONAL CONFERENCE ON QUANTUM PROBABILITY AND RELATED TOPICS
    • Place of Presentation
      Levico Teme-Italy
    • Year and Date
      2011-05-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] Infinite dimensional Laplacians associated with derivatives of an infinite dimensional Brownian Motion2011

    • Author(s)
      K. Saito
    • Organizer
      Chungbuk National University, Korea
    • Place of Presentation
      Invited Lecture
    • Year and Date
      2011-03-19
    • Related Report
      2011 Final Research Report
  • [Presentation] Higher order derivatives of white noise and infinite dimensional Laplacians2010

    • Author(s)
      K. Saito
    • Organizer
      研究集会
    • Place of Presentation
      愛知教育大学
    • Year and Date
      2010-12-27
    • Related Report
      2011 Final Research Report
  • [Presentation] Exotic Laplacians and higher order derivatives of white noise2010

    • Author(s)
      K. Saito
    • Organizer
      The 10^<th> Sendai Workshop on Infinite Dimensional Analysis and Quantum Probability, Graduate School of Information Sciences
    • Place of Presentation
      Tohoku University
    • Year and Date
      2010-12-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Exotic Laplacians and higher order derivatives of white noise2010

    • Author(s)
      K.Saito
    • Organizer
      IDAQP Sendai Seminar
    • Place of Presentation
      Tohoku University
    • Year and Date
      2010-06-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] A Gauss-Poisson correspondence and Laplace operators2009

    • Author(s)
      K. Saito
    • Organizer
      第10回チュニジア-日本文化・科学・技術学術会議TJASST10
    • Place of Presentation
      Tunisia
    • Year and Date
      2009-11-12
    • Related Report
      2011 Final Research Report
  • [Presentation] A Gauss-Poisson correspondence and Laplace operators2009

    • Author(s)
      K.Saito
    • Organizer
      チュニジア-日本文化・科学・技術学術会議 第10回記念大会(TJASSST 10)
    • Place of Presentation
      Tunisia, Mehari Hammamet
    • Year and Date
      2009-11-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] Exotic Laplacians in White Noise Theory2009

    • Author(s)
      K. Saito
    • Organizer
      Invited Lecture at University of Tunis El Manar-Tunisia
    • Place of Presentation
      Tunisia
    • Year and Date
      2009-11-11
    • Related Report
      2011 Final Research Report
  • [Presentation] Exotic Laplacians and higher derivatives of white noise2009

    • Author(s)
      K. Saito
    • Organizer
      大学間共同研究Volterra Center, University of Rome Torvergata
    • Place of Presentation
      Rome, Italy
    • Year and Date
      2009-09-04
    • Related Report
      2011 Final Research Report
  • [Presentation] Exotic Laplacians and exponential functions of white noise2009

    • Author(s)
      K. Saito
    • Organizer
      科研費研究集会
    • Place of Presentation
      福岡教育大学,アブストラクト
    • Year and Date
      2009-09-01
    • Related Report
      2011 Final Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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