• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Mercerian and Tauberian theorems with applications

Research Project

Project/Area Number 12640148
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

INOUE Akihiko  Hokkaido Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (50168431)

Co-Investigator(Kenkyū-buntansha) MAEJIMA Makoto  Keio Univ., Faculty of Sci. and Tech., Prof., 理工学部, 教授 (90051846)
MIKAMI Toshio  Hokkaido Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (70229657)
ARAI Asao  Hokkaido Univ,. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (80134807)
KASAHARA Yuji  Ochanomizu Univ., Faculty of Sci., Prof., 理学部, 教授 (60108975)
Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2001: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2000: ¥2,100,000 (Direct Cost: ¥2,100,000)
KeywordsMercerian theorem / Tauberian theorem / partial autocorrelation function / FARIMA process / prediction theory / long memory / risky asset model / past and future method / 定常過程 / long memory
Research Abstract

Inoue and Bingham developed the theory of ratio Mercerian theorems introduced by themselves. In particular, they showed that ratio Mercerian theorems for systems can be used to prove various Tauberian theorems. For example, they proved Tauberian theorems for general kernels in the boundary case using that theory. They also proved Tauberian and Mercerian theorems for some arithmetic sums using this technique.
Inoue proved a representation theorem for partial autocorrelation functions of stationary time series, using the past and future method introduced by himself. Using the representation theorem, he determined the asymptotics for the partial autocorrelation functions of FARIMA processes, which are popular paremetric long-memory models.
Inoue and Anh introduced a dynamic model of risky asset prices with memory. They developed a theory for the model. In particular, they gave option pricing formulas in the financial market model with this risky asset.

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (66 results)

All Other

All Publications (66 results)

  • [Publications] A.Inoue: "Asy mptotics for the partial autocorrelation function of a stationary process"J. Anal. Math.. 81. 65-109 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Inoue: "Asy mptotics for prediction errors of stationary processes with reflection positivity"J. Math. Anal. Appl.. 250. 299-319 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] N.H.Bingham: "Abelian, Tauberian and Mercerian theorems for arithmetic sums"J. Math. Anal. Appl.. 250. 465-493 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] N.H.Bingham: "Tauberian and Mercerian theorems for systems of kernals"J. Math. Anal. Appl.. 252. 177-197 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Arai: "A particle-field Hamiltonian in relativistic quantum electrodynamics"J. Math. Phys. 41. 4271-4283 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Arai: "Essential spectrum of a self-adjoint operator on abstract Hilbert space of Fock type and applications to quantum field Hamiltonians"J. Math. Anal. Appl.. 246. 189-216 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Arai: "Ground states of a general class of quantum field Hamiltonians"Rev. Math. Phys.. 12. 1085-1135 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Arai: "Infinite dimensional analysis and analytic number theory"Acta Appl. Math.. 63. 41-78 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Arai: "Exact solutions of multi-component nonlinear Schrodinger and Klein-Gordon equations in two-dimensional space-time"J. Phys. A : Math. Gen. 34. 4281-4288 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Arai: "Ground state of the massless Nelson model without infrared cutoff in a non-Fock representation"Rev. Math. Phys.. 13. 1075-1094 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Arai: "Stability of Ground States in Sectors and Its application to the Wigner-Weisskopf Model"Rev. Math. Phys.. 13. 513-527 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Mikami: "Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric"Appl. Math. Optim.. 42. 203-227 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Ishii: "A mathematical model of the wearing process of a nonconvex stone"SIAM J. Math. Anal.. 33. 860-876 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Mikami: "A uniqueness result on Cauchy problem related to jump-type Markov processes with unbounded characteristics"Stoc. Anal. Appl.. 20(発表予定). (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] P.Embrechts: "An introduction to the theory of self-similar stochestic processes"J. Modern Physics B. 14. 1399-1420 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Maejima: "The class of type G distributions on IR^d and related subclasses of infinitely divisible distributions"Demonstratio Mathematica. 34. 251-266 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Maejima: "Type G distributions on IR^d"J. Theor. Probab.. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Kasahara: "Remarks on Tauberian theorem of exponential type and Fenchel-Legendre transform"Osaka J. Math.. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Kasahara: "A remark on the covariance matrix of fractional Brownian motion"Rep. Nat. Sci. Ocha. Univ.. 52. 13-19 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Kasahara: "Large deviation around the origin for sums of nonnegative i.i.d. random vaviables"Rep. Nat. Sci. Ocha. Univ.. 51. 27-31 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 新井朝雄: "フォック空間と量子場 上,下"日本評論社. (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] P.Embrechts: "Selfsimilar Processes"Princeton University Press(発表予定). (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Inoue: "Asymptotics for the partial autocorrelation function of a stationary process"J. Anal. Math.. 81. 65-109 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Inoue: "Asymptotics for prediction errors of stationary processes with reflection positivity"J. Math. Anal. Appl.. 250. 299-319 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] N. H. Bingham: "Abelian, Tauberian and Mercerian theorems for arithmetic sums"J. Math. Anal. Appl.. 250. 465-493 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] N. H. Bingham: "Tauberian and Mercerian theorems for systems of kernels"J. Math. Anal. Appl.. 252. 177-197 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "A particle-field Hamiltonian in relativistic quantum electrodynamics"J. Math. Phys.. 41. 4271-4283 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "Essential spectrum of a self-adjoint operator on an abstract Hilbert space of Fock type and applications to quantum field Hamiltonians"J. Math. Anal. Appl.. 246. 189-216 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "Ground states of a general class of quantum field Hamiltonians"Rev. Math. Phys.. 12. 1085-1135 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "Infinite-dimensional analysis and analytic number theory"Acta Appl. Math.. 63. 41-78 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "Exact solutions of multi-component nonlinear Schrodinger and Klein-Gordon equations in two-dimensional space-time"J. Phys. A : Math. Gen.. 34. 4281-4288 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "the massless Nelson model without infrared cutoff in a non-Fock representation"Rev. Math. Phys.. 13. 1075-1094 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "Stability of ground states in sectors and its application to the Wigner-Weisskopf model"Rev. Math. Phys.. 13. 513-527 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Mikami: "Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric"Appl. Math. Optim.. 42. 203-227 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Ishii: "A mathematical model of the wearing process of a nonconvex stone"SIAM J. Math. Anal.. 33. 860-876 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Mikami: "A uniqueness result on Cauchy problem related to jump-type Markov processes with unbounded characteristics"Stoc. Anal. Appl.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] P. Embrechts: "An introduction to the theory of self-similar stochastic processes"Intern. J. Modern Physics B. 14. 1399-1420 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Maejima: "The class of type G distributions on R^d and related subclasses of infinitely divisible distributions"Demonsratio Mathematica. 34. 251-266 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Maejima: "Type G distributions on R^d"J. Theor. Probab.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Kasahara: "Remarks on Tauberian theorem of exponential type and Fenchel-Legendre tranform"Osaka J. Math.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Kasahara: "A remark on the covariance matrix of fractional Brownian motion"Rep. Nat. Sci. Ocha. Univ.. 52. 13-19 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Kasahara: "Large deviation around the origin for sums of nonnegative i.i.d. random variables"Rep. Nat. Sci. Ocha. Univ.. 51. 27-31 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "Fock space and quantum fields"(in Japanese), Nihonhyouronsha. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] P. Embrechts, M. Maejima: "Selfsimilar processes"Princeton University Press, (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Arai: "Exact Solutions of multi-component nonlinear Schrodinger and Klein-Gordon equations in two-dimensional space-time"J. Phys. A : Math. Gen.. 34. 4281-4288 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] A. Arai: "Ground state on the maesless Nelson model without infrared cutoff in a non-Fock representation"Rev. Math. Phys.. 13. 1075-1094 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] A. Arai: "Stability of ground states in sectors and its application to the Wignor-Weisskopf model"Rev. Math. Phys.. 13. 513-527 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H. Ishii: "A mathematical model of the wearing process of a non convex stone"SIAM J. Math. Anal.. 33. 860-876 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Mikami: "A uniqueness result on Cauchy problem related to jump-type Markov processes with unbounded characteristics"Stoc. Anal. Appl.. 20(発表予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] M. Maejima: "The class of type G distributions on IR^d and related subclass of infinitely divisible distributions"Demonstratio Mathematics. 34. 251-266 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M. Maejima: "Type G distributions on IR^d"J. Theor. Probab.. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y. Kasahara: "Remarks on Tauberian theorem of exponential type and Fenchel-Logendre transform"Osaka J. Math.. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y. Kasahara: "A remark on the covariance matrix of fractional Brownian motion"Rep. Nat. Sci. Ocha. Univ.. 52. 13-19 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] P. Embrechts: "Self similar Processes"Princeton University Press(発表予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] N.H.Bingham: "Tauberian and Mercerian theorems for systems of kernels"J.Math.Anal.Appl.. 252. 177-197 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.H.Bingham: "Abelian, Tauberian, and Mercerian theorems for arithmetic Sums"J.Math.Anal.Appl.. 250. 465-493 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Inoue: "Asymptotics for the partial autocorrelation function of a stationary process"J.Anal.Math.. 81. 65-109 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.H.Bingham: "Extension of the Drasin-Shea-Jordan theorem"J.Math.Soc.Japan. 52. 545-559 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Inoue: "Asymptotics for prediction errors of sationary processes with reflection positivity"J.Math.Anal.Appl.. 250. 299-319 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Arai: "A particle-field Hamiltonian in relativistic quantum electrodynamics"J.Math.Phys.. 41. 4271-4283 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Arai: "Essential spectrum of a self-adjoint operator on an abstract Hilbert space of Focktype and applications to quantum field Hamiltonians"J.Math.Anal.Appl.. 246. 189-216 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Arai: "Ground states of a general class of quantum Hamiltonians"Rev.Math.Phys.. 12. 1085-1135 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Mikami: "Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric"Appl.Math.Optim.. 42. 203-227 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Maejima: "Distributions of selfsimilar and semi-selfsimilar processes with independent increments"Statist.Probab.Lett.. 47. 395-401 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Maejima: "Completely operator semi-selfdecomposable distributions"Tokyo J.Math.. 23. 235-253 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 新井朝雄: "フォック空間と量子場上,下"日本評論社. 636 (2000)

    • Related Report
      2000 Annual Research Report

URL: 

Published: 2000-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi