Large deviations for additive functional of symmetric Markov processes

• Project/Area Number: 21740109
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: 防衛大学校 (2010-2011); Toba National College of Maritime Technology (2009)
• Principal Investigator: TSUCHIDA Kaneharu 防衛大学校, 総合教育学群, 講師 (80466523)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 確率論 / 大偏差原理 / 加法的汎関数 / ジャンプ過程 / ディリクレ形式 / レヴィ過程 / 解析学 / 関数解析学 / 応用数学

Research Abstract

In this study, we prove large deviation principles for additive functionals associated with various symmetric Markov processes. Moreover, we find a sufficient condition to hold the large deviation principle, collect these conditions into a paper. This paper was published in 2011.

Research Products

• [Journal Article] Large deviations for discontinuous additive functionals of symmetric stable processes (2011)
  • Author(s): 土田兼治、竹田雅好
  • Journal Title: Mathematiche Nachrichten Volume: 284 Issue: 8-9 Pages: 1148-1171
  • DOI: 10.1002/mana.200810843
  • Peer Reviewed
• [Journal Article] On a sufficient condition for large deviations of additive functionals (2011)
  • Author(s): 土田兼治
  • Journal Title: Stochastics and Dynamics Volume: 11 Issue: 01 Pages: 157-181
  • DOI: 10.1142/s0219493711003218
  • Peer Reviewed
• [Journal Article] Large deviation for discontinuous additive functional for symmetric stable processes
  • Author(s): M.Takeda, K.Tsuchida
  • Journal Title: Mathematische Nachrichten (掲載決定)
  • Peer Reviewed
• [Journal Article] Large deviation for additive functional with jumps
  • Author(s): K.Tsuchida
  • Journal Title: 数理解析研究所講究録 (掲載決定)
• [Presentation] Differentiability of spectral functions for nearly stable processes (2011)
  • Author(s): 土田兼治
  • Organizer: KKR敬天閣
  • Place of Presentation: KKR敬天閣、鹿児島
  • Year and Date: 2011-11-05
• [Presentation] Differentiability of spectral functions for nearly stable processes (2011)
  • Author(s): 土田兼治
  • Organizer: マルコフ過程と関連する話題
  • Place of Presentation: KKR敬天閣(鹿児島県)
  • Year and Date: 2011-11-05
• [Presentation] 加法的汎関数の大偏差原理が成り立つための十分条件について (2011)
  • Author(s): 土田兼治
  • Organizer: 東京確率論セミナー
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-10-18
• [Presentation] Differentiability of spectral functions for nearly stable processes and large deviations (2011)
  • Author(s): 田原喜宏
  • Organizer: 日本数学会2011年度秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-29
• [Presentation] Large deviations for additive functionals of nearly stable processes (2011)
  • Author(s): 土田兼治
  • Organizer: 東北確率論セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2011-06-17
• [Presentation] Large deviation for additive functionals of nearly stable processes (2011)
  • Author(s): 土田兼治
  • Organizer: 東北確率論セミナー
  • Place of Presentation: 東北大学(宮城県)
  • Year and Date: 2011-06-17
• [Presentation] Large deviations for additive functionals of nearly stable rocesses (2011)
  • Author(s): 土田兼治
  • Organizer: UW Probability seminar、University of Washington
  • Place of Presentation: United States
  • Year and Date: 2011-03-09
• [Presentation] Large deviations for additive functional of nearly stable processes (2011)
  • Author(s): Kaneharu Tsuchida
  • Organizer: UW Probability seminar
  • Place of Presentation: University of Washington(米国)
  • Year and Date: 2011-03-09
• [Presentation] Strong and weak disorder for Levy directed polymer in random environment (2011)
  • Author(s): Kaneharu Tsuchida
  • Organizer: Probability and PDE 2011
  • Place of Presentation: 広島大学(広島県)
  • Year and Date: 2011-01-13
• [Presentation] Strong and weak disorder for Levy Directed polymers in random environment (2011)
  • Author(s): 土田兼治
  • Organizer: Probability and PDE
  • Place of Presentation: 広島大学
• [Presentation] 加法的汎関数の大偏差原理が成り立つための十分条件について (2010)
  • Author(s): 土田兼治
  • Organizer: 東京確率論セミナー
  • Place of Presentation: 東京工業大学(東京都)
  • Year and Date: 2010-10-18
• [Presentation] Large deviations for additive functional of jump type Markov processes (2010)
  • Author(s): 土田兼治
  • Organizer: 第13回広島応用解析セミナー
  • Place of Presentation: 広島大学(広島県)
  • Year and Date: 2010-08-24
• [Presentation] Large deviations for additive functionals of jump type Markov processes (2010)
  • Author(s): 土田兼治
  • Organizer: 第13回広島応用解析セミナー
  • Place of Presentation: 広島大学
• [Presentation] Large deviations for additive functinoals with jumps (2009)
  • Author(s): 土田兼治
  • Organizer: 東北確率論セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2009-06-18
• [Presentation] Large deviations for additive functionals with jumps (2009)
  • Author(s): 土田兼治
  • Organizer: Kyoto RIMS Workshop on Stochastic Analysis of Jump Process and Related Topics
  • Place of Presentation: 京都大学
• [Presentation] Large deviations for discontinuous Additive functionals of symmetric stable processes (2009)
  • Author(s): 土田兼治
  • Organizer: Workshop on Limit Theorems、Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic
  • Place of Presentation: チェコ共和国、プラハ
• [Presentation] Large deviations for additive functional with jumps (2009)
  • Author(s): K.Tsuchida
  • Organizer: Kyoto RIMS Workshop on Stochastic Analysis of Jump Processes and Related Topics
  • Place of Presentation: 京都大学
• [Presentation] Large deviations for discontinuous additive functional of symmetric stalbe processes (2009)
  • Author(s): K.Tsuchida
  • Organizer: Workshop on Limit Theorems
  • Place of Presentation: チェコ共和国プラハInstitute of Information Theory and Automation, Academy of Science of the Czech Republic