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

Construction and Decomposition of Diffusion Processes

Research Project

Project/Area Number 09640274
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 InstitutionYamaguchi University

Principal Investigator

TOMISAKI Matsuyo  Faculty of Education, Yamaguchi University Professor, 教育学部, 教授 (50093977)

Co-Investigator(Kenkyū-buntansha) MASUMOTO Makoto  Faculty of Science, Yamaguchi University Associate Professor, 理学部, 助教授 (50173761)
YANAGIHARA Hiroshi  Faculty of Engineering, Yamaguchi University Associate Professor, 工学部, 助教授 (30200538)
OKADA Mari  Faculty of Engineering, Yamaguchi University Associate Professor, 工学部, 助教授 (40201389)
YANAGI Kenjiro  Faculty of Engineering, Yamaguchi University Professor, 工学部, 教授 (90108267)
KAWAZU Kiyoshi  Faculty of Education, Yamaguchi University Professor, 教育学部, 教授 (70037258)
村木 尚文  山口大学, 工学部, 助教授 (60229979)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,600,000 (Direct Cost: ¥1,600,000)
KeywordsSobolev inequality / diffusion process / Brownian Motion / Dirichlet form
Research Abstract

We investigated construction and decomposition of diffusion processes defined on a domain D (* R^d) whose boundary *D is of Lipschitz with H_lder cusps. *D must be locally expressed as a graph of a H_lder function and the infimum gamma of H_lder exponents must be positive. Let (epsilon, H^1 (D)) be a Dirichiet form corresponding to second order partial differential operator of elliptic type, {G_<lambda> } the strongly continu- ous resolvent on L^2 (D) assosiated with epsilon. Then (i) G_<lambda> (L2(D)*L^p (D)) * C(D), p > 1 + (d- 1)/gamma, and (ii) G_<lambda> (C_* (D)) is a dense subspace of C_* (D). Hence there exists a diffusion process M on D associated with C.This process is a reflecting diffusion process on D.The resolvent as above has a density which is continuous on D chi D off diagonal. Thus M has a transition probability density p(t, x, y) . We can obtain upper bounds of p(t, x, y), which depend on the shape of cusps. Our diffusion pro- cess M is defined on D.Applying a decompositin theorem due to M.Fukushima, sample paths of M admit a unique decomposition : martingale additive functionals and continuous additive functionals locally of zero energy. If coefficients of epsilon is of C^1 (D)-class and H_lder cusps are greater than 1/2 in addition, then continuous additive functionals locally of zero energy are of bounded variation and have Skoro- hod representations. This is an interesting property independ of dimension d. M is also a solution of a submartingale problem. We can prove that the submartingale problem has a unique solution if d = 2 and the coefficients of epsilon are of C^<1, alpha> -class.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (63 results)

All Other

All Publications (63 results)

  • [Publications] M.Tomisaki: "Sobolev inequality on an anti-symmetric cusp domain" Bulletin of the Faculty of Education, Yamaguchi University. 47. 1-12 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Tomisaki: "Limit thoerems for hitting times of 1-dimensional generalized diffusions" Nagoya Math.J.152. 1-37 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Kawazu: "A diffusion process in a Brownian environment with drift" J.Math.Soc.Japan. 49. 189-211 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Kawazu: "Random walks and diffusion processes in a random environment" Sugaku Expositions. 11. 51-75 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Kawazu: "Invariance principle for a Brownian motion with large drift in a white noise environment" Hiroshima Math.J.28. 129-137 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen: "On the Cover's conjecture on capacity of Gaussian channel with feedback" IEICE Trans.Fundamentals. E80-A. 2272-2275 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Yanagi: "On the Cover's conjecture of Gaussian feedback capacity" Proceeding on 1997 International Symposium on Information Theory. 130-130 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen: "Factor-of-two bound for capacity in Gaussian channel with feedback and Cover's conjecture" Proceedings of the China and Japan Joint Symposium on Applied Functional Analysis and Related Topics. 32-45 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen: "Refinement of factor-of-two bound for Gasussian feedback capacity" Proceedings of the 20th Symposium on Information Theory and its Application. 229-232 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Yanagi: "An upper bound to the capacity of discrete time Gaussian channel with feedback III" Bull.Kyushu Inst.Tech.Pure and Applied Mathematics. 45. 1-8 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen: "Refinement of factor-of-two bound for capacity in Gasussian channels with feedback and related inequality" Proceedings on 1998 International Symposium on Information Theory. 128-128 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen: "Refinement of upper bound on capacity of Gaussian channel with blockwise white noise" Proceedings of the 21st Symposium on Information Theory and its Application. 391-394 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen: "Refinements of the half-bit and factor-of-two bounds for capacity in Gasussian channels with feedback" IEEE Trans.Information Theory. IT-45 印刷中. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Matusu-Necasova: "Free Boundary Problem for the Equation of Spherically Symmetric Motion of Viscous Gas(III)" Japan Journal of Industrial and Applied Mathematics. 14. 199-213 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Bonk: "Distortion theorems for Bloch functions" Pacific J.of Math.179. 241-262 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Muraki: "Noncommutative Brownian motion in monotone Fock space" Commun.Math.Phys.183. 557-570 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Muraki: "Independence conditional expectation and martingales in permutational Fock space" Quantum Probability Communications. 10. 261-280 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Masumoto: "Extremal lengths of homology classes on Riemann surfaces" J.Reine Angew.Math.508 印刷中. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Tomisaki: "Sobolev inequality on an anti-symmetric cusp domain" Bulletin of the Faculty of Education, Yamaguchi University. 47. 1-12 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Tomisaki and M.Yamazato: "Limit theorems for hitting times of 1-dimensional generalized diffusions" Nagoya Math.J.152. 1-37 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Kawazu and H.Tanaka: "A diffusion process in a Brownian environment with drift" J.Math.Soc.Japan. 49. 189-211 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Kawazu: "Random walks and diffusion processes in a random environment" Sugaku Expositions. 11. 51-75 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Kawazu and H.Tanaka: "In variance principle for a Brow-nian motion with large drift in a white noise environment" Hiroshima Math.J.28. 129-137 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen and K.Yanagi: "On the Cover's conjecture on capacity of Gaussian channel with feedback" IEICE Trans.Fundamentals. E80-A. 2272-2275 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Yanagi: "On the Cover's conjecture of Gaussian feedback capacity" Proceeding on 1997 International Symposium on Information Theory. 130 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen and K.Yanagi: "Factor-of-two bound for capac-ity in Gaussian channel with feedback and Cover's conjecture" Proceedings of the China and Japan Joint Symposium on Applied Functional Analysis and Related Topics. 32-45 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen and K.Yanagi: "Refinement of factor-of-two bound for Gasussian feedback capacity" Proceedings of the 20th Symposium on Information Theory and its Application. 229-232 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Yanagi: "An upper bound to the capacity of discrete time Gaussian channel with feedback, III" Bull.Kyushu Inst.Tech., Pure and Applied Mathematicscation. 45. 1-8 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen and K.Yanagi: "Refinement of factor-of-two bound for capacity in Gasussian channels with feedback and related inequality" Proceedings on 1998 International Symposium on Information Theory. 128 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen and K.Yanagi: "Refinement of upper bound on capacity of Gaussian channel with blockwise white noise" Proceedings of the 21st Symposium on Information Theory and its Application. 391-394 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Han Wu Chen and K.Yanagi: "Refinement of the half-bit and factor-of-two bounds for capacity in Gasussian channels with feedback" IEEE Trans.Information Theory. IT-45 (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Matusu-Necasova, M.Okada and T.Makino: "Free Boundary Problem for the Equation of Spherically Symmetric Mo-tion of Viscous Gas (III)" Japan Journal of Industrial and Applied Mathematics. 14. 199-213 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Bonk, D.Minda and H.Yanagihara: "Distortion theorems for Bloch functions" Pacific J.of Math.179. 241-262 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Muraki: "Noncommutative Brownian motion in monotone Fock space" Commun.Math.Phys.183. 557-570 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Muraki: "Independence, conditional expectation, and mar-tingales in permutational Fock space" Quantum Probability Communications. 10. 261-280 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Masumoto: "Extremal lengths of homology classes on Rie-mann surfaces" J.Reine Angew.Math.508 (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Tomisaki: "Sobolev inequality on an anti--symmetric cusp domain" Bulletin of the Faculty of Education,Yamaguchi University. 47,Pt.2. 1-11 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Tomisaki: "Limit theorems for hitting times of 1-dimensional generalized diffusions" Nagoya Math.J.152(発表予定). (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Kawazu: "Random walks and diffusion processes in a random environment" Sugaku Expositions AMS. 11・1. 51-75 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Kawazu: "Invariance principle for a Brownian motion with large drift in a white noise environment" Hiroshima Math.J. 28. 129-137 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Kawazu: "A diffusion process in a random environment with drift" J.Math.Soc.Japan. 49. 189-211 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Yanagi: "An upper bound to the capacity of discrete time Gaussian channel with feedback,III" Bull.Kyushu Inst.Tech.,Pure and Applied Mathematics. 45. 1-8 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Han Wu Chen: "Coverのconjectureに関連した結果" 数理解析研究所講究録. 1039. 111-117 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Han Wu Chen: "Factor-of-two bound for capacity in Gaussian channel with feedback and Cover's conjecture" Proceedings of the China and Japan Joint Symposium on Applied Functional Analysis and Related Topics. (発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Han Wu Chen: "Refinements of the half-bit and factor-of-two bounds for capacity in Gaussian channels with feedback" IEEE Trans.Information Theory. (発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] 柳研二郎: "無限時限空間上の確率測度に関連する再生核ヒルベルト空間の役割-連続時間ガウス型通信路への応用をにらんで-" 数理解析研究所講究録. 1067. 108-117 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Han Wu Chen: "情報理論における通信路容量についてのある不等式について,II" 1998年度実解析シンポジウム報告集. (発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Han Wu Chen: "Refinement of upper bound on capacity of Gaussian channel with blockwise white noise" Proceedings of the 1998 Symposium on Information Theory and its Application. (発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Sarka Matusu-Necasova: "Free Boundary Problem for the Equation of Spherically Symmetric Motion of Viscous Gas (III)" Japan Journal of Industrial and Applied Mathematics. 14・2. 199-213 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Bonk: "Distortion theorems for Bloch functions" Pacific J.of Math.179. 241-262 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Masumoto: "Extremal lengths of homology classes on Riemann surfaces" J.Reine Angew.Math.(発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Tomisaki: "Sobolev inequality on an anti-symmetric cusp domain" Bulletin of the Faculty of Education,Yamagushi University. 42. 1-12 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Kawazu: "A diffusion process in a Brownian environment with drift" J.Math.Soc.Japan. 49. 189-211 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.W.Chen: "On the Cover's conjecture on Capacity of Gaussian channel with feedback" IEICE Transactions on Fundamentals. E80-A・11. 2272-2275 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 陳 漢武: "Coverのconjectureに関連した結果" 京都大学数理解析研究所講究録. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] H.W.Chen: "Factor-of-two bound for capacity in Gaussian channel with feedback and Cover's conjecture" Proceedings of the China and Japan Joint Symposium on Applied Functional Analysis and Related Topics. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 陳 漢武: "情報理論における通信路容量についてのある不等式について" 実解析シンポジウム報告集. 132-145 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.W.Chen: "Refinement of factor-of-two bound for Gaussian channel capacity" Proceedings of the 1997 Symposium on Information Theory and its Application. 20. 229-232 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Yanagi: "An upper bound to the capacity of discrete time Gaussian channel with feedback,III" Bull.Kyushu Inst.Tech.,Pure.Appl.Math.(発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Matusu-Necasova: "Free Boundary Problem for the Equation of Spherically Symmetric Motion of Viscous Gas(III)" Japan Journal of Industial and Applied Mathematics. 12・2. 199-213 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Bonk: "Distortion estimates for locally univalent Bloch functions" Pacific J.of Math. 179・2. 241-262 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Muraki: "Noncommutative Brownian motion in monotone Fock space" Communications in Mathematical Physics. 183. 557-570 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Muraki: "Independence,conditional expectation,and martingales in permutational Fock space" Quantum Probability Communications. (発表予定).

    • Related Report
      1997 Annual Research Report

URL: 

Published: 1997-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi