Limit theorems of functionals for Markov processes and their applications

• Project/Area Number: 23740073
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto Sangyo University (2012-2015); Kyoto University (2011)
• Principal Investigator: YANO Yuko 京都産業大学, 理学部, 准教授 (10337462)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 確率論 / 確率過程論 / マルコフ過程 / 拡散過程 / 加法過程 / 極限定理 / 一般化逆正弦法則 / 処罰問題

Outline of Final Research Achievements

I studied some limit theorems of functionals for Markov processes and obtained the following results: I studied asymptotic behavior of the law of the occupation time for Brownian motion and random walks on fractals (joint work with N. Kajino et al.); I obtained some remarkable results for the joint law of occupation times for a diffusion process on multiray; I showed the new method to calculate special values of the Hurwitz zeta function via generalized Cauchy variables (joint work with T. Fujita); I succeeded to obtain a sigma-finite measure unifying supremum penalisations for a stable Levy process; I studied h-transforms of one-dimensional diffusions stopped upon hitting zero (joint work with K. Yano); I studied local time penalisations with various random clocks (joint work with C. Profeta et al.).

Research Products

• [Int'l Joint Research] イヴリ=ヴァル=デソンヌ大学/パリ第六大学(フランス)
• [Int'l Joint Research] シンシナティ大学(米国)
• [Journal Article] On the joint law of the occupation times for a diffusion process on multiray (2016)
  • Author(s): Yuko Yano
  • Journal Title: Journal of Theoretical Probability Volume: 未定 Issue: 2 Pages: 490-509
  • DOI: 10.1007/s10959-015-0654-4
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On h-transforms of one-dimensional diffusions stopped upon hitting zero (2015)
  • Author(s): Kouji Yano and Yuko Yano
  • Journal Title: Seminaire de Probabilites Volume: 47
  • NAID: 120006305986
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Local time penalizations with various clocks (2015)
  • Author(s): Christophe Profeta・矢野孝次・矢野裕子
  • Journal Title: 確率論シンポジウム・数理解析研究所講究録 Volume: 未定
• [Journal Article] 一次元拡散過程に対する原点回避条件付け (2015)
  • Author(s): 矢野孝次・矢野裕子
  • Journal Title: 統計数理研究所共同研究リポート・無限分解可能過程に関連する諸問題 Volume: 19
  • NAID: 120005593676
• [Journal Article] A remarkable sigma-finite measure unifying supremum penalisations for a stable Levy process (2013)
  • Author(s): Yuko Yano
  • Journal Title: Annales de l'Institut Henri Poincare, Probabilites et Statistiques Volume: 49 Issue: 4 Pages: 1014-1032
  • DOI: 10.1214/12-aihp497
  • Peer Reviewed
• [Journal Article] Special values of the Hurwitz zeta function via generalized Cauchy variables (2012)
  • Author(s): Takahiko Fujita and Yuko Yano
  • Journal Title: Kyoto Journal of Mathematics Volume: 52 Issue: 3 Pages: 465-477
  • DOI: 10.1215/21562261-1625163
  • Peer Reviewed
• [Journal Article] マルチレイ上の拡散過程の滞在時間同時分布 (2012)
  • Author(s): 矢野裕子
  • Journal Title: 統計数理研究所共同研究リポート Volume: 275
• [Presentation] ブラウン処罰問題について (2014)
  • Author(s): 矢野裕子
  • Organizer: 確率論早春セミナー
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] マルチレイ上の拡散過程の滞在時間同時分布 (2012)
  • Author(s): 矢野裕子
  • Organizer: 非正則な拡散過程における諸問題(招待講演)
  • Place of Presentation: 奈良女子大学
• [Presentation] On the law of the occupation time for Brownian motion on fractals (2012)
  • Author(s): 矢野裕子
  • Organizer: Stochastic Analysis and its Applications(招待講演)
  • Place of Presentation: 新潟大学
• [Presentation] On the law of the occupation time for Brownian motion on the Sierpinski gasket (2011)
  • Author(s): 矢野裕子
  • Organizer: 5th International Conference on Stochastic Analysis and its Applications(招待講演)
  • Place of Presentation: ボン大学（ドイツ，ボン）
• [Presentation] フラクタル上のブラウン運動の片側滞在時間分布について (2011)
  • Author(s): 矢野裕子
  • Organizer: 日本数学会秋季総合分科会統計数学分科会
  • Place of Presentation: 信州大学
• [Presentation] マルチレイ上の拡散過程の滞在時間同時分布 (2011)
  • Author(s): 矢野裕子
  • Organizer: 日本数学会秋季総合分科会統計数学分科会
  • Place of Presentation: 信州大学
• [Presentation] マルチレイ上の拡散過程の滞在時間同時分布 (2011)
  • Author(s): 矢野裕子
  • Organizer: マルコフ過程と関連する話題(招待講演)
  • Place of Presentation: KKR鹿児島敬天閣
• [Presentation] マルチレイ上の拡散過程の滞在時間同時分布 (2011)
  • Author(s): 矢野裕子
  • Organizer: 統計数理研究所共同研究集会無限分解可能過程に関連する諸問題
  • Place of Presentation: 統計数理研究所（東京都立川市）