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

Progress in new methods for prediction theory and Tauberian theorems with applications to stochastic analysis of processes with memory

Research Project

Project/Area Number 16340030
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

INOUE Akihiko  Hokkaido Univ., Fac.of Sci., Asso.Prof., 大学院理学研究院, 助教授 (50168431)

Co-Investigator(Kenkyū-buntansha) NAKAZI Takahiko  Hokkaido Univ., Fac.of Sci., Prof., 大学院理学研究院, 教授 (30002174)
KASAHARA Yukio  Hokkaido Univ., Fac.of Sci., Researcher, 大学院理学研究院, 学術研究員 (10399793)
三上 敏夫  北海道大学, 大学院・理学研究科, 助教授 (70229657)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥13,600,000 (Direct Cost: ¥13,600,000)
Fiscal Year 2006: ¥5,600,000 (Direct Cost: ¥5,600,000)
Fiscal Year 2005: ¥5,600,000 (Direct Cost: ¥5,600,000)
Fiscal Year 2004: ¥2,400,000 (Direct Cost: ¥2,400,000)
KeywordsPrediction theory / Orthogonal polynomials / Verblunsky coefficients / Long memory / Financial market model with memory / Long term investment / Partial autocorrelation function / Duality in prediction theory / 効用等値価格 / 記憶を持つ確立過程 / 予測問題 / 確率解析 / 記憶を持つ確率過程 / 最適投資問題 / フィルタリング / 非マルコフ型ノイズ
Research Abstract

(1)Inoue and Nakano solved two long term investment problems in a financial market model with memory. They are maximization of expected growth rate and that of large deviation probability. They also studied the parameter estimation.
(2)Inoue and Nakano extended the results of (1). The result admits monotone increasing term structure of volatility. In so doing, the key is to solve Riccati-type equations.
(3)Inoue, Kasahara and Pourahmadi obtained new results concerning prediction when finite number of data are missing.
(4)Inoue, Kasahara and Pourahmadi introduced a finite dimensional duality in prediction theory and studied its properties. Using the duality, they unified the results of Kolmogorov, Yaglom and Nakazi, and also extended them.
(5)Inoue, Kasahara and Bingham gave a new definition of long memory based on OPUC and also related results. This definition gives a wider class of long memory processes than thosed based on the integrability of covariance. FARIMA is a typical example. They obtained new results for FAIMA based on this new definition.
(6)Inoue and Anh proved an analogue of representation theorems in finite prediction in discrete time.for continuous time, long memory model with stationary increments. Using it, they also proved an analogue of Baxter's inequality.
(7)Inoue, Fukuda and Nakano developed a new theory of indifference pricing and, using it, obtained new results on pricing of financial and insurance products. In particular, they obtained new results when the utility function is of exponential type.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (60 results)

All 2007 2006 2005 2004 Other

All Journal Article (60 results)

  • [Journal Article] Prediction of fractional Brownian motion-type proesses2007

    • Author(s)
      Akihiko Inoue
    • Journal Title

      Stochastic Analysis and Applications 25

      Pages: 641-666

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Optimal long-term investment model with memory2007

    • Author(s)
      Akihiko Inoue
    • Journal Title

      Applied Mathematics and Optimization 55

      Pages: 93-122

    • NAID

      120000965233

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Binary market models with memory2007

    • Author(s)
      Akihiko Inoue
    • Journal Title

      Statistics & Probability Letters 77

      Pages: 256-264

    • NAID

      120000967157

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A Prediction Problem in L^2(w)2007

    • Author(s)
      Mohsen Pourahmadi
    • Journal Title

      Proceedings of the American Mathematical Society 135

      Pages: 1233-1239

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Finite dimensional semisimple Q-algebras2007

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Linear Algebra and its Applications 420

      Pages: 407-423

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Optimal long-term investment model with memory2007

    • Author(s)
      A.Inoue
    • Journal Title

      Applied Mathematics and Optimization 55

      Pages: 93-122

    • NAID

      120000965233

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Binary market models with memory2007

    • Author(s)
      A.Inoue
    • Journal Title

      Statistics & Probability Letters 77

      Pages: 256-264

    • NAID

      120000967157

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A Prediction Problem in L^2 (w)2007

    • Author(s)
      M.Pourahmadi
    • Journal Title

      Proceedings of the American Mathematical Society 135

      Pages: 1233-1239

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Explicit representation of finite predictor coefficients and its applications2006

    • Author(s)
      Akihiko Inoue
    • Journal Title

      The Annals of Statistics 34

      Pages: 973-993

    • NAID

      120000972661

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Linear filtering of systems with memory and application to finance2006

    • Author(s)
      Akihiko Inoue
    • Journal Title

      Journal of Applied Mathematics and Stochastic Analysis 2006

      Pages: 1-26

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Isometric composition operators between two weighted Hardy spaces2006

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Nihonkai Mathematical Journal 17

      Pages: 111-124

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Double commuting compressed shifts and generalized interpolation in the Hardy space over the bidisk2006

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Integral Equations and Operator Theory 56

      Pages: 543-558

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Explicit representation of finite predictor coefficients and its applications2006

    • Author(s)
      A.Inoue
    • Journal Title

      The Annals of Statistics 34

      Pages: 973-993

    • NAID

      120000972661

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Explicit representation of innovation processes with application to optimal investment model with memory2006

    • Author(s)
      A.Inoue
    • Journal Title

      RIMS Kokyuroku 1491

      Pages: 46-59

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Linear filtering of systems with memory and application to finance2006

    • Author(s)
      A.Inoue
    • Journal Title

      Journal of Applied Mathematics and Stochastic Analysis 2006

      Pages: 1-26

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Isometric composition operators between two weighted Hardy spaces2006

    • Author(s)
      T.Nakazi
    • Journal Title

      Nihonkai Math. J. 17

      Pages: 111-124

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Double commuting compresset shifts and generalized interpolation in the Hardy space over the bidisc2006

    • Author(s)
      T.Nakazi
    • Journal Title

      Integr. equ. oper. theory 56

      Pages: 543-558

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Explicit representation of finite predictor coefficients and its applications2006

    • Author(s)
      A.Inoue
    • Journal Title

      The Annals of Statistics 34・(印刷中)

    • NAID

      120000972661

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Financial markets with memory I : Dynamic models2005

    • Author(s)
      Vo Anh
    • Journal Title

      Stochastic Analysis and Applications 23

      Pages: 275-300

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Financial markets with memory II : Innovation processes and expected utility maximization2005

    • Author(s)
      Vo Anh
    • Journal Title

      Stochastic Analysis and Applications 23

      Pages: 301-328

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Rouche type theorems and a theorem of Adamyan, Arov and Krein2005

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Mathematica Scandinavica 97

      Pages: 154-160

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Interpolation of weighted l^q sequences by H^p functions2005

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Taiwanese Journal of Mathematics 9

      Pages: 457-467

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Invariant subspaces and Hankel-type operators on a Bergman space2005

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Proceedings of the Edinburgh Mathematical Society 48

      Pages: 479-484

    • NAID

      120000963348

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Financial markets with memory I Dynamic models2005

    • Author(s)
      Vo Anh
    • Journal Title

      Stochastic Analysis and Applications 23

      Pages: 275-300

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Financial markets with memory II : Innovation processes and expected utility maximi7atirm2005

    • Author(s)
      Vo Anh
    • Journal Title

      Stochastic Analysis and Applications 23

      Pages: 301-328

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Interpolation of weighted I^q sequences by HAP functions2005

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Taiwanese Journal of Mathematics 9

      Pages: 457-467

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Financial markers with memory I : Dynamic models2005

    • Author(s)
      A.Inoue
    • Journal Title

      Stochastic analysis and applications 23・2

      Pages: 275-300

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Financial markwes with memory II : Innovation processes and expected utility maximization2005

    • Author(s)
      A.Inoue
    • Journal Title

      Stochastic analysis and applications 23・2

      Pages: 301-328

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Interpolation of weighted l^8 sequences by H^P functions2005

    • Author(s)
      T.Nakazi
    • Journal Title

      Tainanese Journal of Mathematics 9・3

      Pages: 457-467

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Invariance subspaces and Hankel-type operaters on a Bergman space2005

    • Author(s)
      T.Nakazi
    • Journal Title

      Proceedings of the Edinburgh Mathematical Sociery 48

      Pages: 479-484

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Rouche type theorem and a theorem of Adamyan, Arov and Krein2005

    • Author(s)
      T.Nakazi
    • Journal Title

      Mathematica Scandiavica 97・

      Pages: 154-160

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Prediction of fractional Brownian motion with Hurst index less than 1/22004

    • Author(s)
      Vo Anh
    • Journal Title

      Bulletin of the Australian Mathematical Society 70

      Pages: 321-328

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing2004

    • Author(s)
      Akihiko Inoue
    • Journal Title

      Journal of Multivariate Analysis 89

      Pages: 135-147

    • NAID

      120000969604

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Backward shift invariant subspaces in the bidisc. III2004

    • Author(s)
      Keiji Izuchi
    • Journal Title

      Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum 70

      Pages: 727-749

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Brown-Halmos type theorems of weighted Toeplitz operators. II2004

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Far East Journal of Mathematical Sciences (FJMS) 13

      Pages: 343-355

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Backward shift invariant subspaces in the bidisc. II2004

    • Author(s)
      Keiji Izuchi
    • Journal Title

      Journal of Operator Theory 51

      Pages: 361-376

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Factorizations of functions in H^p(T^n)2004

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Complex Variables. Theory and Application. An International Journal 49

      Pages: 323-329

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Invariant subspaces of finite codimension and uniform algebras2004

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Glasgow Mathematical Journal 46

      Pages: 117-120

    • NAID

      120000956153

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Backward shift invariant subspaces in the bidisc2004

    • Author(s)
      Keiji Izuchi
    • Journal Title

      Hokkaido Mathematical Journal 33

      Pages: 247-254

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Backward shift invariant subspace in the bidisc. II2004

    • Author(s)
      Keiji Izuchi
    • Journal Title

      Journal of Operator Theory 51

      Pages: 361-376

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Factorizations of functions in H^p(T^n))2004

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Complex Variables. Theory and Application. An International Journal 49

      Pages: 323-329

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing2004

    • Author(s)
      A.Inoue
    • Journal Title

      J.Multivariate Anal. 89

      Pages: 135-147

    • NAID

      120000969604

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Prediction of fractional Brownian motion with Hurst index less than 1/22004

    • Author(s)
      V.Anh
    • Journal Title

      Bull.Austral.Math.Soc. 70

      Pages: 321-328

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Backward shift invariant subspaces in the bidisc2004

    • Author(s)
      K.Izuchi
    • Journal Title

      Hokkaido Math.J. 33

      Pages: 247-254

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Backward shift invariant subspaces in the bidisc II2004

    • Author(s)
      K.Izuchi
    • Journal Title

      J.Operator Th. 51

      Pages: 361-376

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Factorization of functions in H^P(T^n)2004

    • Author(s)
      T.Nakazi
    • Journal Title

      Complex Variables Th.and Appl. 49

      Pages: 323-329

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Invariant subspaces of finite codimension and uniform algebras2004

    • Author(s)
      T.Nakazi
    • Journal Title

      Glasgow Math.J. 46

      Pages: 117-120

    • NAID

      120000956153

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Brown-Halmos type theorems of weighted Toeplitz operators II2004

    • Author(s)
      T.Nakazi
    • Journal Title

      Far East J.Math.Sci. 13

      Pages: 343-355

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Nonnegative functions in weighted hardy spaces2004

    • Author(s)
      J.Inoue
    • Journal Title

      Complex Variables Th.and Appl. 49

      Pages: 837-843

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Backward shift invariant subspaces in the bidisc III2004

    • Author(s)
      K.Izuchi
    • Journal Title

      Acta.Sci.Math. 70

      Pages: 727-749

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A level set approach of the wearing process of a nonconvex stone2004

    • Author(s)
      H.Ishii
    • Journal Title

      Calc.Var.Partial Differential Equations 19

      Pages: 53-93

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Motion of a graph by R-curvature2004

    • Author(s)
      H.Ishii
    • Journal Title

      Arch.Ration.Mech.Anal. 171

      Pages: 1-23

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Monge's problem with a quadratic cost by the zero-noise limit of h-path processes2004

    • Author(s)
      T.Mikami
    • Journal Title

      Probab.Theory Related Fields 129

      Pages: 245-260

    • NAID

      120000954971

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Covariance kernel and the central limit theorems in the total variation distance2004

    • Author(s)
      T.Mikami
    • Journal Title

      J.Multivariate Anal. 90

      Pages: 257-268

    • NAID

      120000964098

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Convexified Gauss curvature flow of sets : A stochastic approximation2004

    • Author(s)
      H.Ishii
    • Journal Title

      SIAM J.Math.Anal. 36

      Pages: 552-579

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Financial markets with memory I : Dynamic models

    • Author(s)
      V.Anh
    • Journal Title

      Stochastic Anal.Appl. 発表予定

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Financial markets with memory II : Innovation processes and expected utility maximization

    • Author(s)
      V.Anh
    • Journal Title

      Stochast.Anal.Appl. 発表予定

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Interpolation Of Weighted lq Sequences By H^p Functions

    • Author(s)
      T.Nakazi
    • Journal Title

      Taiwanese J.Math. 発表予定

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Rouche type theorems and a theorem of Adamyan, Aeov and Krein

    • Author(s)
      T.Nakazi
    • Journal Title

      Math.Scand. 発表予定

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Invariant subspaces and Hankel type operators on a Bergman space

    • Author(s)
      T.Nakazi
    • Journal Title

      Proc.Edinburgh Math.Soc. 発表予定

    • NAID

      120000963348

    • Related Report
      2004 Annual Research Report

URL: 

Published: 2004-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi