Study on the time-dependence structure of completely nondeterministic stationary processes

• Project/Area Number: 18740065
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Hokkaido University
• Principal Investigator: KASAHARA Yukio Hokkaido University, 大学院理学研究院, 学術研究員 (10399793)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,740,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 定常過程 / 偏相関係数 / 完全非決定性 / 単位円上の直交多項式 / 関数解析 / 関数論 / 確率論

Research Abstract

定常過程、正確に言うと弱定常過程ですが、これは記憶を持つ確率過程(時間と共に変動する偶然量の数学的模型)で、予測問題を含めて、過去と未来の間の依存関係が主な研究対象になります。
私は特に、局所的な時間発展を支配する偏相関係数と呼ばれる量に興味があります。
本研究では、完全非決定性という性質に着目し、それに付随する特性量を用いた表現や漸近挙動の特徴付けなど、偏相関係数に関連する幾つかの結果が得られました。

Research Products

• [Journal Article] Baxter's inequality for fractional Brownian motion-type processes with Hurst index less than 1/2 (2008)
  • Author(s): Akihiko Inoue, Yukio Kasahara and Punam Phartyal
  • Journal Title: Statistics & Probability Letters 78 Pages: 2889-2894
  • NAID: 120006459591
  • Peer Reviewed
• [Journal Article] Baxter's inequality for fractional Brownian motion-type processes with Hurst index less than 1/2 (2008)
  • Author(s): Akihiko Inoue, Yukio Kasahara, Punam Phartyal
  • Journal Title: Statistics & Probability Letters 78 Pages: 2889-2894
  • NAID: 120006459591
  • Peer Reviewed
• [Journal Article] Duals of random vectors and processes with applications to prediction problems with missing values
  • Author(s): Yukio Kasahara, Mohsen Pourahmadi and Akihiko Inoue
  • Journal Title: Statistics & Probability Letters
  • Peer Reviewed
• [Presentation] Orthogonal polynomials on the unit circle associated with a rigid function (2) (2008)
  • Author(s): 笠原雪夫
  • Organizer: 実解析学シンポジウム2008
  • Place of Presentation: 山口大学
  • Year and Date: 2008-11-09
• [Presentation] Orthogonal polynomials on the unit circle associated with a rigid function (2008)
  • Author(s): 笠原雪夫
  • Organizer: 実解析学シンポジウム2008
  • Place of Presentation: 山口大学
  • Year and Date: 2008-11-09
• [Presentation] OPUC under the Levinson-Mckean condition, Verblunsky coefficients and phase coefficients (2008)
  • Author(s): 笠原雪夫
  • Organizer: 日本数学会, 秋季総合分科会, 統計数学分科会,
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] OPUC under the Levinson-McKean condition, Verblunsky coefficients and phase coefficients (2008)
  • Author(s): 笠原雪夫
  • Organizer: 日本数学会秋季総合分科会統計数学分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] A duality relation in some prediction problems (2007)
  • Author(s): 笠原雪夫
  • Organizer: 実解析学シンポジウム2007
  • Place of Presentation: 大阪教育大学
  • Year and Date: 2007-10-20
• [Presentation] 定常過程の予測問題と直交多項式 (2007)
  • Author(s): 笠原雪夫
  • Organizer: 第46回実関数論・函数解析学 合同シンポジウム
  • Place of Presentation: 九州大学
  • Year and Date: 2007-08-08
• [Presentation] 定常過程の予測問題と直交多項式 (2007)
  • Author(s): 笠原 雪夫
  • Organizer: 第46回実関数論・函数解析学合同シンポジウム
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2007-08-08
• [Presentation] Orthogonal polynomials on the unit circle associated with a rigid function (2006)
  • Author(s): 笠原雪夫
  • Organizer: 実解析学シンポジウム2006
  • Place of Presentation: 弘前大学
  • Year and Date: 2006-10-28