Research of dam processes based on the theory of infinitely divisible processes.

2002 Fiscal Year Final Research Report Summary

• Project/Area Number: 12640113
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Shinshu University
• Principal Investigator: INOUE Kazuyuki Shinshu University, Faculty of Science, Prof., 理学部, 教授 (70020675)
• Co-Investigator(Kenkyū-buntansha): MATSUGU Yasuo Shinshu University, Faculty of Science, Prof., 理学部, 教授 (60020682) ; HATTORI Kumiko Shinshu University, Faculty of Science, Ass. Prof., 理学部, 助教授 (80231520) ; HONDA Katsuya Shinshu University, Faculty of Science, Prof., 理学部, 教授 (50109302) ; WATANABE Toshiro The University of Aizu, Center for Mafe. Sci., Lect., 総合数理科学センター, 講師 (50254115) ; SATO Ken-iti Nagoya University, Emeritus Prof., 名誉教授
• Project Period (FY): 2000 – 2002
• Keywords: infinitely divisible processes / multiparameter Levy processes / random measures / dam processes / storage processes / Markov chains

Research Abstract

We are concerned with venous topics on Levy processes and infinitely divisible processes. The joint work of K. Sato and T. Watanabe clarified the transience levels for Levy processes by using the moments of last exit times. The problem of recurrence-transience for selfsimilar additive processes was discussed in the joint work of Sato and K. Yamamuro. Sato introduced the notion of multiparameter Levy processes with time parameter moving in the positive orthant of a Euclidean space. He studied the hereditary property of selfdecomposability for the multivariate subordination of multiparameter Levy processes. K. Inoue extended the class of multiparameter Levy processes by dropping the time homogenous property of their increments. He described these processes by infinitely divisible random measures and provided the condition for the selfsimilarity. Sato also investigated the relation between cone-parameter Levy processes and convolution semigroups. Inoue introduced a stochastic model for a dam with non-additive and periodic input. He investigated the limiting behavior of the hidden Markov chain when the dam process is characterized by linear release rate function. The nonlinear case was partially solved.

Research Products

• [Publications] K.Inoue(共著): "The limiting behavior of a dam process with periodic input"統計数理研究所 共同研究リポート. 127. 53-56 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 井上 和行: "A class of multiparameter Levy processes"統計数理研究所 共同研究リポート. 137. 83-87 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 井上 和行: "A class of multiparameter Levy processes of Gaussian type"統計数理研究所 共同研究リポート. 146. 7-12 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Inoue: "Multiparameter additive processes of mixture type"統計数理研究所 共同研究リポート. 157. 99-106 (2003)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] M.Maejima(共著): "Completely operator semi-selfdecomposable distributions"Tokyo J. Math. 23. 235-253 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] M.Maejima(共著): "Distributions of selfsimilar and semi-selfsimilar processes with independent increments"Statistics and Probability Letters. 47. 395-401 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato: "Density Transformation in Levy processes"MaPhySto Lecture Notes, No.7. 91 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato(共著): "Recurrence transience for selfsimilar additive processes associated with stable distributions"Acta Mathematicae. 63. 375-384 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] O.E.Barndorff-Nielsen(共著): "Multivariate subordination, selfdecomposability and stability"Adv. Appl. Probab.. 33. 160-187 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato: "Subordination and selfdecomposability"Statistice and Probability Letters. 54. 317-324 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] J.Pedersen(共著): "Levy processes and convolution semigroups with parameter in a cone"Mini-proceedings : 2nd MaPhySto Conference on Levy Processes : Theory and Applications. 221-227 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] M.Maejima(共著): "Semi-Levy processes semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlenliech type processes"J. Math. Kyoto Univ.. (出版予定).
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 佐藤健一: "Paul Levy "Theorie de l'Addition des Variable Aleatoires"には何が書いてあるか"統計数理研究所 共同研究リポート. 127. 1-14 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato: "Lebesgue decomposition between two path space measures induced by Levy processes"統計数理研究所 共同リポート. 137. 1-10 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato: "Multivariate subordination and selfdecomposability"統計数理研究所 共同研究リポート. 137. 23-28 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato(共著): "Last exit times for transient Levy processes (preliminary report)"統計数理研究所 共同研究リポート. 137. 72-82 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato: "Levy processes and convolution semigroups with parameter in a cone"統計数理研究所 共同研究リポート. 146. 1-6 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato: "On a theorem on Levy processes"統計数理研究所 共同研究リポート. 146. 33-37 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 佐藤 健一: "加法過程による積分と半Levy過程へのその応用"統計数理研究所 共同研究リポート. 157. 1-5 (2003)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 前島 信(共著): "半Levy過程,半自己相似加法過程,および半定常Ornstein-Uhlenbeck型過程"統計数理研究所 共同研究リポート. 157. 6-11 (2003)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Watanabe: "Shift self-similar additive random sequences associated with supercritical branching processes"J. Theoretical Probability. 15(3). 631-665 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Watanabe: "Limit theorems for shift selfsimilar additive random sequences"Osaka J. Math. 39. 561-603 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Watanabe: "Absolute continuity of some semi-selfdecomposable distributions and self-simiter measures"Probab. Theory Related Fields. 117(3). 387-405 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Watanabe: "Continuity properties of distributions with some decomposability"J. Theoretical Probability. 13(1). 169-191 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Watanabe: "Shift selfsimilar random sequences with independent increments"統計数理研究所 共同研究リポート. 127. 61-67 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Watanabe: "Shift selfsimilar additive random sequences associated with supercritical branchiby processes"統計数理研究所 共同研究リポート. 137. 35-42 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 渡部 俊朗: "多次元無限分解可能分布の漸近挙動"統計数理研究所 共同研究リポート. 146. 94-97 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 渡部 俊朗: "Exact packing measure on the boundary of a Galton-Watson tree"統計数理研究所 共同研究リポート. 157. 40-46 (2003)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 志村 隆彰(共著): "Infinite divisibility and generalized sulexponentiality"統計数理研究所 共同研究リポート. 157. 118-135 (2003)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Hattori: "Exact Hausdorff dimension of self-avoiding processes on the multi-dimensional siepisk : gasket"Journal of Math. Science, Univ. Tokyo. 7. 57-98 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] B.Hambly(共著): "Self-repelling walk on the Sierprinski gasket"Pabability Theory and Related Fields. 124. 1-25 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 服部久美子: "Self-repelling walks on the Sierpinski Gasket"統計数理研究所 講究録. 1275. 112-118 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 松山 貴(共著): "Edwards-Wilkinson方程式の解の分散について"日本応用数理学会論文誌. 11(2). 87-102 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] S.Iwasaki(共著): "How many blocks can children pile up? scaling and universality for a simple play"J. Physical Soc. Japan. 69(6). 1579-1581 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] Y.Matsugu: "Invariant subspaces of the Privalev spaces"Far East J. Math. Sci.. 2(4). 633-643 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] Y.Matsugu(共著): "Isometries of weighted Bergman-Privalov spaces on the unit ball of C^n"J. Math. Soc. Japan. 54(2). 341-347 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] Y.Matsugu(共著): "A characterization of weighted Bergman-Orlicz spaces on the unit ball in C^n"J. Austral. Math. Ser. A. (印刷中).
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] Y.Matsugu(共著): "A characterization of weighted Bergman-Privalos spaces on the unit ball of C^n"J. Korean Math. Soc.. 39(5). 783-800 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 真次康夫: "(log^+)pの不変部分空間"数理解析研究所 講究録. 1137. 57-60 (2000)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 真次康夫(共著): "Privalov空間の準同型"数理解析研究所 講究録. 1243. 30-44 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 真次康夫(共著): "C^nの単位球B上のkim空間"数理解析研究所 講究録. 1277. 120-135 (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Sato(共著): "Levy Processes : Theory and Applications(pp.3-37)"Birkkauser(edited by O.E.Barndorff-Nielsen et al.). 35 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] A.Rocha-Arteage(共著): "Topics in Infinitely Divisible Distributions and Levy Processes"Communication Tecnica CIMAT. 107 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Watanabe(共著): "Levy Processes : Theory and Applications(pp.89-107)"Birkhauser,(edited by O.E. Barndorff-Nielsen et al.). 19 (2001)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 本田勝也: "フラクタル"朝倉書店. (2002)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K.Honda(共著): "Recent Research Developments in Physics"Transworld Research Network(印刷中). (2003)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] K. INOUE et al.: "The limiting behavior of a dam process with periodic input."The Institute of Statistical Mathematics, Cooperative Research Report. 127. 53-56 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. INOUE: "Multiparameter additive processes of mixture type."The Institute of Statistical Mathematics, Cooperative Research Report. 157. 99-103 (2003)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] M. MAEJIMA et al.: "Completely operator semi-selfdecomposable distributions."Tokyo J. Math.. 23. 235-253 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] M. Maejima et al.: "Distribulions of selfsimilar and semi-selfsimilar processes with independent increments."Statistics and Probability Letters. 47. 395-401 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato et al.: "Recurrence-t ansience for selfsimilar additive processes associated with stable distributions."Acta Mathematicae. 63. 375-384 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] O. E. Barndorff-Nielsen et al.: "Multivariate subordination, selfdecomposability and stability."Adv. Appl. Probab.. 33. 160-187 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato: "Subordination and selfdecomposability."Statistics and Probability Letters. 54. 317-324 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] J. Pedersen: "Levy processes and convolution semi-groups with parameter in a cone."Mini-proceedings: 2nd MaPhySto Conference on Levy Processes: Theory and Applications. 221-227 (2002)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] M. Maejima et al.: "Semi-Levy processes, semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlenbeck type processes."J. Math. Kyoto Univ.. (in press)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato: "Lebesgue decom tosition between two path space measures induced by Levy processes."The Institute of Statistical Mathematics, Cooperative Research Report. 137. 1-10 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato: "Multivariate subordination-and selfdecomposability."The Institute of Statistical Mathematics, Cooperative Research Report. 137. 23-28 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato: "Last exit times for transient Levy processes (preliminary report)."The Institute of Statistical Mathematics, Cooperative Research Report. 137. 72-82 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato: "Levy processes and convolution semigroups with parameter in a cone."The Institute of Statistical Mathematics, Cooperative Research Report. 146. 1-6 (2002)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato: "On a theorem on Levy processes."The Institute of Statistical Mathematics, Cooperative Research Report. 146. 33-37 (2002)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato: "Density transformation in Levy processes."MaPhySto Lecture Notes. Vol.7. 91 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] A. Rocha-Arteaga et al.: "Topics in Infinitely Divisible Distributions and Levy Processes."Communication Tecnica CIMAT. 107 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T. Watanabe: "Shift self-similar additive random sequences associated with supercritical branching processes."J. Theoretical Probability. 15(3). 631-665 (2002)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T. Watanabe: "Limit theorems for shift selfsimilar additive random sequences."Osaka J. Math.. 39. 561-603 (2002)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T. Watanabe: "Absolute continuity of some semi-selfdecomposable distributions and self-similar measures."Probab. Theory Related Fields. 117(3). 387-405 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T. Watanabe: "Continuity properties of distributions with some decomposability."J. Theoretical Probability. 13(1). 169-191 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T. Watanabe: "Shift selfsimilar random sequences with independent increments."The Institute of Statistical Mathematics, Cooperative Research Report. 127. 61-67 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T. Watanabe: "Shift selfsimilar additive random sequences associated with supercritical branching processes."The Institute of Statistical Mathematics, Cooperative Research Report. 137. 35-42 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Hattori: "Exact Hausdorff dimension of self-avoiding processes on the multidimensional Sierpinski gasket."Journal of Mathematical Sciences, University of Tokyo. 7. 57-98 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] B. Hambly et al.: "Self-repelling walk on the Sierpinski gasket"Probab. Theory Related Fields. 124. 1-25 (2002)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] S. Iwasaki et al.: "How many blocks can children pile up? - Scaling and universal ity for a simple play -"J. Phys. Soc. Japan. 69(6). 1579-1581
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Honda et al.: "On the Kardar-Parisi-Zhang Equation for growing rough surfaces."Recent Reasearch Developments in Physics, Transworld Research Network. (in press)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] Y. Matsugu: "Invariant subspaces of the Privalov spaces."Far East J. Math. Sci.. 2(4). 633-643 (2000)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] Y. Matsugu et al.: "Isometries of weighted Bergman-Privalov spaces on the unit ball of C"."J. Math. Soc. Japan. 54(2). 341-347 (2002)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] Y. Matsugu et al.: "A characterization of weighted Bergman-Privalov spaces 01 the unit ball of C"."J. Korean Math. Soc.. 39(5). 783-800 (2002)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Sato: "Basic results in Levy processes., Levy Processes, Theory and Applications, (edited by O.E.Barndorff-Nielsen et al.)"Birkhauser. 3-37 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T. Watanabe: "Temporal change in distributional properties of Levy processes., Levy Processes, Theory and Applications,"Birkhauser. 89-107 (2001)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] K. Honda: ""Fractal" (in Japanese)."Asakura Shoten. (2002)
  • Description: 「研究成果報告書概要(欧文)」より