Quantitative analysis of reversible Markov processes and the theory of stochastic stopping game

可逆马尔可夫过程的定量分析和随机停止博弈理论

• 批准号: 15540142
• 负责人: FUKUSHIMA Masatoshi
• 金额: $ 1.79万
• 依托单位: Kansai University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540142/
• 关键词: symmetric Markov process; Dirichlet form; time changed process; Feller measures; scale function; excursion; Poisson point process; stopping game; ダグラス積分; 定量解析; 対称安定過程; スペクトル総合; 確率停止ゲーム理論

The head investigator collaborated with J. Ying and X. Fang to characterize all regular Dirichlet subspaces of a one-dimensional Sobolev space in terms of a family of scale functions in the joint paper from Osaka J. Math. He also successfully collaborated with J. Ying and P. He and then with J. Ying and Z.Q.Chen to characterize the jumping measure of the time changed processes of a symmetric diffusion and a most general symmetric Markov process in terms of the Feller measure determined by the minimal process, and the results are being published in two papers from Annales of Probability in USA. He further collaborates with H. Tanaka to extend an old result of K. Ito by construction a symmetric diffusion by piecing together excursions away from a point in a joint paper being published in a famous French journal.

首席研究员与J.Ying和X.方舟子刻画了一个正则Dirichlet子空间的所有特征，在Osaka J.Math.的联合论文中，他用一族标度函数定义了一维Sobolev空间。他还成功地与J.Ying和P.He合作，然后与J.Ying和Z.Q.Chen合作，用Feller测度刻画了对称扩散和最一般对称Markov过程的时变过程的跳跃测度用最小过程确定，结果发表在美国概率年鉴的两篇论文中。他还与H。Tanaka推广了K.伊藤通过构建一个对称的扩散拼凑在一起的游览远离一个点在一个联合文件正在发表在一个著名的法国杂志。

项目成果

Time changes of symmetric diffusions and Feller measures

• DOI: 10.1214/009117904000000649
• 发表时间: 2004-10
• 期刊: Annals of Probability
• 影响因子: 2.3
• 作者: M. Fukushima;P. He;J. Ying

M.Fukushima, T.Uemura: "On spectral synthesis for contractive p-norms and Besov spaces"Potential Analysis. 20. 195-206 (2004)

M.Fukushima、T.Uemura：“关于收缩 p 范数和 Besov 空间的谱合成”潜力分析。

On regular Dirichlet subspaces of H1(I) and associated linear diffusions

• DOI: 10.1515/9783110215250.443
• 发表时间: 2010-01
• 作者: N. Jacob;Y. Oshima;M. Takeda

M.Fukushima, T.Uemura: "Capacitory bounds of measures and ultracontractivity of time changed processes"J.Math.Pures Appl.. 82. 553-572 (2003)

M.Fukushima、T.Uemura：“测量的电容界限和时间变化过程的超收缩性”J.Math.Pures Appl.. 82. 553-572 (2003)

M.Fukushima, P.He, J.Ying: "Time changes of symmetric diffusions and Feller measures"Annales Probability. (印刷中). (2004)

M.Fukushima、P.He、J.Ying：“对称扩散的时间变化和费勒测度”年鉴概率（2004 年出版）。