New development of excursion theory for Markov processes

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20740060
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto University (2011); Kobe University (2008-2010)
• Principal Investigator: YANO Kouji Kobe University, 理学研究科, 准教授 (80467646)
• Project Period (FY): 2008 – 2011
• Keywords: マルコフ過程 / ブラウン運動 / 周遊理論

Research Abstract

マルコフ過程のエクスカーション(以下,周遊)理論とは,複雑な様相を呈するマルコフ過程の標本路を与えられた点を起終点とする道の断片に分割して得られた周遊点過程の確率論的振る舞いを明らかにする理論であり,標本路の再帰構造を究明する強力な理論である.
本研究の目的は,マルコフ過程の周遊理論を新しい視点から発展させることである.具体的な問題として,マルコフ過程(特に,拡散過程及びレヴィ過程)の極限定理への応用,弱流出境界を持つ消滅ポテンシャルつき拡散過程の標本路の構成,周遊の成す凸集合の端点集合の決定問題,に取り組む.

Research Products

• [Journal Article] Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups. (2010)
  • Author(s): T.Hirayama, K.Yano.
  • Journal Title: Stochastic Process.Appl. 120, no.8 Pages: 1404-1423
  • Peer Reviewed
• [Journal Article] Cameron-Martin formula for the σ-finite measure unifying Brownian penalisations. (2010)
  • Author(s): K.Yano.
  • Journal Title: J.Funct.Anal. 258, no.10 Pages: 3492-3516
  • Peer Reviewed
• [Journal Article] Excursions away from a regular point for one-dimensional symmetric Levy processes without Gaussian part. (2010)
  • Author(s): K.Yano.
  • Journal Title: Potential Anal. 32, no.4 Pages: 305-341
  • Peer Reviewed
• [Journal Article] Penalising symmetric stable Levy paths. (2009)
  • Author(s): K.Yano, Y.Yano, M.Yor.
  • Journal Title: J.Math.Soc.Japan 61, no.3 Pages: 757-798
  • Peer Reviewed
• [Journal Article] Realization of ergodic Markov chain as a random walk subject to a synchronizing road coloring.
  • Author(s): K.Yano, K.Yasutomi.
  • Journal Title: J.Appl.Probab. (掲載決定)
  • Peer Reviewed
• [Presentation] 離散時刻確率方程式の強い解と強くない解について (2011)
  • Author(s): 矢野孝次
  • Organizer: Dynamics of complex systems 2011 -時間発展の非可逆性と予測可能性の限界に関する諸分野からの提言-
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-03-07
• [Presentation] Extremality of excursion measure and of σ-finite measure unifying penalisations (2010)
  • Author(s): 矢野孝次
  • Organizer: 34th Conference on Stochastic Processes and their Applications
  • Place of Presentation: 千里ライフサイエンスセンター
  • Year and Date: 2010-09-07
• [Presentation] Penalising stable Levy paths (2010)
  • Author(s): 矢野孝次
  • Organizer: 4th International Conference on Stochastic Analysis and its Applications
  • Place of Presentation: 関西大学
  • Year and Date: 2010-09-03
• [Presentation] Stochastic equations indexed by negative integers and taking values in compact groups (2009)
  • Author(s): 矢野孝次
  • Organizer: Mathematical Finance and Related Topics in Economics and Engineering
  • Place of Presentation: 関西セミナーハウス
  • Year and Date: 2009-08-15
• [Presentation] Excursions away from a regular point for one-dimensional symmetric Levy processes without Gaussian part (2008)
  • Author(s): 矢野孝次
  • Organizer: Stochastic Analysis and Applications
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2008-09-11
• [Remarks] 論文リストを公開しているホームページ
  • URL: http://www.math.kobe-u.ac.jp/~kyano/works.html