Analysis of functionals of stable processes depending on new noise

• Project/Area Number: 23540153
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Aichi Prefectural University
• Principal Investigator: SI Si 愛知県立大学, 情報科学部, 教授 (70269687)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: ホワイトノイズ / 新ノイズ / 安定仮定 / 重複度 / ポアソン型 / 安定過程 / イタリア、ローマ / White noise / New noise / Stable process / Multiple Markov property / 超汎関数 / 双対生

Research Abstract

Our idea of the research of random complex phenomena is the so-called reductionism. We first obtain a system of independent random variables that contain the same information as that of the given random system so that the given random phenomena can be expressed as functions of the independent random variables just formed. We are ready to carry on the analysis of those functions in question. We have confirmed that the probability distributions of the system of independent random variables are limited either Gaussian or Poisson type under reasonable assumptions. We have studied the latter case where not so well known, and obtained good applications to stable stochastic processes.

Research Products

• [Journal Article] Boundary of homogeneors chaos (2014)
  • Author(s): Si Si
  • Journal Title: Volterra publication Volume: N.640 Pages: 1-8
• [Journal Article] Graded rings of Homogeneous Chaos generated by polynomials in noises depending on time and space parameters respectively (2014)
  • Author(s): Si Si
  • Journal Title: Volterra publication Volume: N.638 Pages: 1-14
• [Journal Article] Graded rings of homogeneous chaos generated by polynomials in noises depending on time and space parameters, respectively (2014)
  • Author(s): Si Si
  • Journal Title: Centro Vito Volterra Publication Volume: N638 Pages: 1-14
  • Peer Reviewed
• [Journal Article] An additive system of idealized random Variables generated by new noise (2014)
  • Author(s): Si Si
  • Journal Title: Centro Vito Volterra Publication Volume: N639 Pages: 1-8
  • Peer Reviewed
• [Journal Article] Boundary of homogeneous chaos (2014)
  • Author(s): Si Si
  • Journal Title: Centro Vito Volterra Publication Volume: N640 Pages: 1-8
  • Peer Reviewed
• [Journal Article] New noise with space parameter and its application (2013)
  • Author(s): Si Si
  • Journal Title: Proceedings of the International Conference on "From Quantum Information to Bio- Informatics, " Quantum Bio-Informatics V. QP-PQ, World Scientific Pub Pages: 291-301
• [Journal Article] H. Poincare's contribution to probability theory (2013)
  • Author(s): Si Si
  • Journal Title: Proceedings of Symposium on History of Mathematics Volume: 35 Pages: 265-274
  • Peer Reviewed
• [Journal Article] A noise with the space parameter and invariance of the class of intensities (2012)
  • Author(s): Si Si
  • Journal Title: Infinite Dimensional Analysis and Quantum Probabilities Volume: Vol.15
• [Journal Article] A Noise with space parameter and representation of SL_2(R) (2012)
  • Author(s): Si Si
  • Journal Title: 電子ジャーナル, 数理解析研究所, 京都大学 Soryusironkenkyu Volume: Vol.13, No.1 Pages: 266-275
• [Journal Article] A noise of new type and its applications (2012)
  • Author(s): T. Hida, Si Si and Win Win Htay,
  • Journal Title: Ricerche di Matematica, Springer Volume: Vol. 61 Pages: 47-55
  • Peer Reviewed
• [Journal Article] Topics on stochastic analysis (2012)
  • Author(s): T. Hida and Si Si,
  • Journal Title: 素粒子論研究 Volume: Vol. 13, No. 1, Pages: 247-259
  • Peer Reviewed
• [Journal Article] Representation of SL2(R) using a noise (2012)
  • Author(s): Si Si
  • Journal Title: 素粒子論研究 Volume: Vol. 13, No. 1, Pages: 266-275
  • Peer Reviewed
• [Journal Article] A noise with space parameter and invariance of the class of intensities (2012)
  • Author(s): K-S. Lee and Si Si
  • Journal Title: Infinite dimensional Analysis, Quantum Probability and Related Topics Volume: Vol. 15.No. 4 Pages: 1-8
  • Peer Reviewed
• [Journal Article] Discrete approximation to operators in white noise analysis (2011)
  • Author(s): Si Si
  • Journal Title: Quantum Probability and White noise analysis,Quantum Bio-Informatics IV Volume: Vol. 28 Pages: 311-320
  • Peer Reviewed
• [Journal Article] A noise of new type and its application (2011)
  • Author(s): T. Hida, Si Si and Win Win Htay
  • Journal Title: Ricerche di matematica、Springer Publ. Co. Volume: On Line journal Issue: 1 Pages: 1-9
  • DOI: 10.1007/s11587-011-0114-0
  • Peer Reviewed
• [Journal Article] Levy の安定過程からベキ乗分布へ (2011)
  • Author(s): Si Si
  • Journal Title: Proｃeedings of Symposium on History of mathematics Research center of Computational Math. Science有 Volume: 32 Pages: 136-145
  • Peer Reviewed
• [Journal Article] A New Noise with space parameter and its characteristic properties
  • Author(s): Si Si
  • Journal Title: Proceedings of 32nd International Conference on Quantum Probability and Related Topics Volume: (accepted, to appear)
• [Presentation] New noise depending on the space parameter and the concept of multiplicity (2014)
  • Author(s): Si Si
  • Organizer: International workshop on IDAQP and related topics
  • Place of Presentation: Institute for Mathematical Sciences, National University of Singapore
  • Invited
• [Presentation] An additive system of idealized random Variables generated by new noise (2013)
  • Author(s): Si Si
  • Organizer: International conference ``QP 34 – Quantum Probability and Related Topics
  • Place of Presentation: Steklov Institute of Mathematics, Moscow
  • Invited
• [Presentation] Personel and academic life of William Feller (2013)
  • Author(s): Si Si
  • Organizer: Symposium on History of Mathematics
  • Place of Presentation: Tsudajuku University, Tokyo
• [Presentation] An additive system of idealized random variables generated by new noise (2013)
  • Author(s): Si Si
  • Organizer: Third QBIC Workshop
  • Place of Presentation: Tokyo university od Science
  • Invited
• [Presentation] Bondary of homogeneous chaos (2013)
  • Author(s): Si Si
  • Organizer: ＱＢＩＣ国際workshop,
  • Place of Presentation: Tokyo Science University
  • Invited
• [Presentation] A noise with space parameter and invariance of the class of intensities (2012)
  • Author(s): Si Si
  • Organizer: International Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: Chungbuk National University, Korea
  • Invited
• [Presentation] H. Poincare's contribution to probability theory (2012)
  • Author(s): Si Si
  • Organizer: 数学歴史研究会,
  • Place of Presentation: 津田塾大学
• [Presentation] New noise with space parameter and its application (2011)
  • Author(s): Si Si
  • Organizer: International Conference on Quantum Information and Bio-information(招待講演)
  • Place of Presentation: Tokyo Science University
• [Presentation] A New Noise and its transformations (2011)
  • Author(s): Si Si
  • Organizer: International Conference on Quantum Information and Probability and Related Topics(招待講演)
  • Place of Presentation: Levico,Trento, Italy
• [Presentation] Some of the recent topics on white noise theory (2011)
  • Author(s): T. Hida and Si Si
  • Organizer: International Conference on Quantum Information and Probability and Related Topics(招待講演)
  • Place of Presentation: Levico,Trento, Italy
• [Book] Introduction to Hida Distributions (2011)
  • Author(s): Si Si
  • Total Pages: 253
  • Publisher: World Scientific Pub. Co
• [Book] 情報社会学議論 (2011)
  • Author(s): 吉田民人、飛田武幸、Si Si他 （公文俊平 編集）
  • Total Pages: 282
  • Publisher: NTT出版
• [Remarks] 国際学会のオーガナイザーInternational Workshop on IDAQP Jan. 7-9, 2013 : 愛知県立大学国際学会の副オーガナイザーIDAQP and Applications March 3-7, 2014, IMS National Univ. of Singapore