Researchers Database

TAKEMURA Tomoko

FacultyFaculty Division of Natural Sciences Research Group of Mathematics
PositionAssociate Professor
Last Updated :2022/10/06

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Profile and Settings

  • Name (Japanese)

    Takemura
  • Name (Kana)

    Tomoko

Research Interests

  • 調和変換
  • ディリクレ形式
  • 斜積拡散過程
  • 拡散過程
  • 極限定理
  • harmonic transform
  • Dirichlet Form
  • skew product diffusion
  • diffusion process
  • Limit theorem

Research Areas

  • Natural sciences, Applied mathematics and statistics
  • Natural sciences, Basic mathematics, probability, Stochastic processes

Research Experience

  • Jan. 2019, 9999, Nara Women's University, 准教授
  • Oct. 2010, Dec. 2018, -:奈良女子大学, 助教
  • 2010, -:Nara Women's University

Education

  • Apr. 2007, Mar. 2010, Nara Women's University, Graduate School of Humanities and Sciences, 博士後期課程 複合現象科学専攻, Japan
  • Apr. 2005, Mar. 2007, Nara Women's University, Graduate School of Humanities and Sciences, 博士前期課程 数学専攻
  • Apr. 2002, Mar. 2005, Nara Women's University, Faculty of Science, 数学科

Association Memberships

  • 日本数学会
  • Mathematical Society of Japan

Ⅱ.研究活動実績

Published Papers

  • Refereed, 2022, 37, 119, 125

MISC

  • Refereed, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, Jump measure densities corresponding to Brownian motion on an annulus, TAKEMURA Tomoko, 2018, 33, 123, 132
  • Refereed, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, 奈良女子大学大学院人間文化研究科, Exponent of inverse local time for harmonic transformed process, TAKEMURA Tomoko; Matsuyo TOMISAKI, We are concerned with inverse local time at regular end points for harmonictransform of a one dimensional diffusion process, and consider the corresponding exponents aswell as the entrance law and the excursion law associated with inverse local time. In 1964 K.Itô and H. P. McKean showed that the Lévy measure density corresponding to the inverselocal time at the regular end point for a recurrent one dimensional diffusion process isrepresented as the Laplace transform of the spectral measure corresponding to the diffusionprocess, where the absorbing boundary condition is posed at the end point. We demonstratethat their representation theorem is available for a transient one dimensional diffusion process,and deduce a representation theorem of the Lévy measure density corresponding to theinverse local time for a transient harmonic transformed process. Furthermore, we show arelation between exponents of inverse local time by means of 0-Green functions and those bymeans of Dirichlet forms, along with correlations between entrance laws of the originaldiffusion processes and its harmonic transform or between excursion laws and the harmonictransform. Moreover we present a new consideration for harmonic transform of non-minimalprocesses., 2016, 31, 31, 127, 138
  • Refereed, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, 奈良女子大学大学院人間文化研究科, The weak mutation and strong selection limit of the Moran model satisfies the strong Markov property, Tomoko TAKEMURA; Matsuyo TOMISAKI; Masaru IIZUKA, The Moran model in population genetics is a one-dimensional generalized diffusionprocess. The weak mutation and strong selection limit process of the Moran model is not a onedimensionalgeneralized diffusion process, but rather a one-dimensional bi-generalized diffusionprocess. One-dimensional bi-generalized diffusion processes are Markov processes, but notnecessarily strong Markov processes, whereas one-dimensional generalized diffusion processesare strong Markov processes. The problem whether the weak mutation and strong selectionlimit process satisfies the strong Markov property remains. This study shows that the limitprocess has a strong Markov property., 2015, 30, 105, 112
  • Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, Asymptotic behavior of Levy measure density corresponding to inverse local time, Tomoko Takemura; Matsuyo Tomisaki, For a one dimensional diffusion process D*(s,m) and the harmonic transformed process D*(sh,mh), the asymptotic behavior of the Levy measure density corresponding to the inverse local time at the regular end point is investigated. The asymptotic behavior of n*, the Levy measure density corresponding to D*(s,m) follows from asymptotic behavior of the speed measure m. However, that of n(h*), the Levy measure density corresponding to D*(sh,mh), is given by a simple form, n* multiplied by an exponential decay function, for any harmonic function h based on the original diffusion operator., Jan. 2015, 91, 1, 9, 13
  • Refereed, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, On the convergence of weak mutation limits of the Moran model in population genetics, TAKEMURA Tomoko; Matsuyo TOMISAKI; Masaru IIZUKA, 2014, 29, 131, 140
  • Refereed, Publications of the Research Institute for Mathematical Sciences, Lévy measure density corresponding to inverse local time, Tomoko Takemura; Matsuyo Tomisaki, We are concerned with the Lévy measure density corresponding to the inverse local time at the regular end point for a harmonic transform of a one-dimensional diffusion process. We show that the Lévy measure density is represented as the Laplace transform of the spectral measure corresponding to the original diffusion process, where the absorbing boundary condition is posed at the end point whenever it is regular. © 2013 Research Institute for Mathematical Sciences, Kyoto University., 2013, 49, 3, 563, 599
  • Refereed, POTENTIAL ANALYSIS, SPRINGER, Convergence of Time Changed Skew Product Diffusion Processes, Tomoko Takemura, A limit theorem for the time changed skew product diffusion processes is investigated. Skew product diffusion processes are given by one dimensional diffusion processes and the spherical Brownian motion, and the time change is based on a positive continuous additive functional. It is shown that the limit process is corresponding to Dirichlet form of non-local type according to degeneracy of the limit measure of underlying ones. Some examples of limit processes are given which lead us to Dirichlet forms with diffusion term, jump term and killing term., Jan. 2013, 38, 1, 31, 55
  • Refereed, KYUSHU JOURNAL OF MATHEMATICS, KYUSHU UNIV, FAC MATHEMATICS, h TRANSFORM OF ONE-DIMENSIONAL GENERALIZED DIFFUSION OPERATORS, Tomoko Takemura; Matsuyo Tomisaki, We are concerned with two types of h transform of one-dimensional generalized diffusion operators treated by Maeno (2006) and by Tomisaki (2007). We show that these two types of h transform are in inverse relation to each other in some sense. Further, we show that a recurrent one-dimensional generalized diffusion operator cannot be represented as an h transform of another one-dimensional generalized diffusion operator different from the original one. We also consider a spectral representation of elementary solutions corresponding to h transformed one-dimensional generalized diffusion operators., Mar. 2012, 66, 1, 171, 191
  • Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, Recurrence/transience criteria for skew product diffusion processes, Tomoko Takemura; Matsuyo Tomisaki, We give recurrence/transience criteria for skew products of one dimensional diffusion process and the spherical Brownian motion with respect to a positive continuous additive functional of the former one dimensional diffusion process. Further we give recurrence/transience criteria for their time changed processes., Jul. 2011, 87, 7, 119, 122
  • Refereed, Osaka Journal of Mathematics, Osaka University and Osaka City University, Departments of Mathematics, Feller property of skew product diffusion processes, TAKEMURA Tomoko, 2011, 48, 1, 269, 290
  • Refereed, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, State of boundaries for harmonic transforms of one-dimensional generalized diffusion processes, TAKEMURA Tomoko, 2009, 25, 285, 294
  • Refereed, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, Elementary solution of Bessel processes with boundary condition, TAKEMURA Tomoko, 2007, 23, 265, 278
  • RIMS Kokyuroku, Kyoto University, Levy measure density corresponding to inverse local time (Probability Symposium), Tomisaki Matsuyo; Takemura Tomoko, Oct. 2013, 1855, 23, 27
  • Refereed, ANNUAL REPORTS OF GRADUATE SCHOOL OF HUMANITIES AND SCIENCES, Silverstein extensions of Dirichlet forms associated with one-dimensional diffusions, Tomoko TAKEMURA; Matsuyo TOMISAKI, Mar. 2022, 37, 119, 125

Presentations

  • 日本数学会2018年度年会, Convergence of diffusion processes in a tube, 2018
  • KWMS International Conference 2017, Convergence for diffusions in balls whose diameter changes, 2017
  • KWMS International Conference 2017, Convergence for diffusions in balls whose diameter changes, 2017
  • World Congress in Probability and Statistics, Exponent of Levy processes corresponding to inverse local time for harmonic transformed diffusion processes, 2016
  • World Congress in Probability and Statistics, Exponent of Levy processes corresponding to inverse local time for harmonic transformed diffusion processes, 2016
  • 6th International Conference on Stochastic Analysis and its Applications, L ́evy measure density corresponding to inverse local time, 2012
  • 日本数学会, L ́evy measure density corresponding to inverse local time, 2012
  • "Stochastic Analysis and Applications" German-Japanese bilateral research project, L ́evy measure density corresponding to inverse local time, 2012
  • 6th International Conference on Stochastic Analysis and its Applications, L ́evy measure density corresponding to inverse local time, 2012
  • "Stochastic Analysis and Applications" German-Japanese bilateral research project, L ́evy measure density corresponding to inverse local time, 2012
  • 日本数学会, 一次元広義拡散過程のh変換, 2011
  • 5th International Conference on Stochastic Analysis and its Applications, Recurrence/transience criteria for skew product diffusion processes, 2011
  • 5th International Conference on Stochastic Analysis and its Applications, Recurrence/transience criteria for skew product diffusion processes, 2011
  • 日本数学会, Convergence of skew product diffusion processes, 2010
  • 日本数学会, 斜積拡散過程の再帰性について, 2010
  • 日本数学会, h変換された一次元広義拡散過程の大域的性質, 2009
  • First Institute of Mathematical Statistics Asia Pacific Rim Meeting, Some property of harmonic transformed one dimensional generalized diffusion processes, 2009
  • 33rd Conference on Stochastic Processes and Their Applications, Feller property and Limit theorem of skew product diffusions, 2009
  • First Institute of Mathematical Statistics Asia Pacific Rim Meeting, Some property of harmonic transformed one dimensional generalized diffusion processes, 2009
  • 33rd Conference on Stochastic Processes and Their Applications, Feller property and Limit theorem of skew product diffusions, 2009
  • 日本数学会, 一次元拡散過程とS^1上のブラウン運動の斜積について, 2008

Awards

  • 人間文化研究科奨励賞, 奈良女子大学, 嶽村 智子, Mar. 2008

Research Projects

  • Grant-in-Aid for Young Scientists (B), Apr. 2014, Mar. 2018, 26800060, Superposition of diffusion processes on a high-dimensional Tube, TAKEMURA TOMOKO, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), Nara Women's University, 2340000, 1800000, 540000, We considered Limit theorems for diffusion processes on a high-dimensional tube. The sequence of diffusion processes are given by direct product diffusion processes D and Y and the time changed diffusion processes where D is a one-dimensional diffusion process and Y is a skew product diffusion of a one-dimensional diffusion process R and d-1 dimensional spherical Brownian motion by means of positive continuous additive functional of R. We show a limit theorem for a sequence of time changed process under some assumptions for underlying measures and we also obtained concrete expressions of the Dirichlet forms corresponding to time changed processes, which may be of non-local type on a tube caused by degeneracy of the underlying measures., url
  • Grant-in-Aid for Scientific Research (C), Apr. 2013, Mar. 2016, 25400139, Coinvestigator, Study of bi-generalized diffusion processes by means of limits of generalized diffusion processes, Tomisaki Matsuyo; TAKEMURA Tomoko; IIZUKA Masaru, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Nara Women's University, 4680000, 3600000, 1080000, We considered properties of bi-generalized diffusion processes which are limits of generalized diffusion processes. We showed that weak mutation limits of the Moran model cannot be weak convergence limits in the space of cadlag functions, though they satisfy the strong Markov property. In the case that the limit of sequence of scale functions and that of speed measure functions have common discontinuous points, we showed that there exists a limit process whose state space has no topological structure. This result indicates that it is necessary to consider properties of bi-generalized diffusion processes by means of limit distributions instead of topological structure of state space., url
  • Grant-in-Aid for JSPS Fellows, 2009, 2010, 09J07274, 斜積拡散過程列の極限についての包括的な研究, 嶽村 智子, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows, Nara Women's University, 1400000, 1400000, 昨年度に引き続き、多様なモデルに対応する確率過程の構築を目指し、その性質を研究することを目的とし、研究を行った。昨年度の成果をもとに、斜積拡散過程と調和変換に関して研究を行った。一次元拡散過程と球面上のブラウン運動によって構成される斜積拡散過程を考察し、コンパクト多様体の内部を運動し、境界ではジャンプや消滅が起こりうる過程に対する再帰性の判定法について結果を得る事ができた。これは、昨年度取り扱った極限定理で現れる極限過程に対応する過程についての再帰性の判定法である。斜積拡散過程に対する再帰性については、今までも議論はあったが、斜積拡散過程を構成する過程と斜積を構成する測度の性質から斜積拡散過程の再帰性を判定するものであり、斜積拡散過程の性質から斜積拡散過程を構成する過程についての性質を得るというものについては研究がなされていなかった。本研究では、一次元拡散過程と球面上のブラウン運動との斜積拡散過程を取り扱う事により、一次元拡散過程の再帰性と斜積拡散過程の再帰性が一対一に対応していることがわかった。この結果は、球面上のブラウン運動という非常に良い性質をもつ過程を取り扱ったことにより得る事ができるが、球面上のブラウン運動に限らず、コンパクト多様体に関しても同様の結果を得ることができる事が予想される。これらの研究により、多様なモデルを取り扱うことができ、力学モデルの分野において応用が期待される。 また、調和変換と呼ばれる場に依存する確率過程の変換について研究を行った。
  • Grant-in-Aid for Scientific Research (C), Apr. 2021, Mar. 2025, 21K12191, Coinvestigator, 数理ゲームを題材とする確率的最適化の研究および機械学習の有効性判定への活用, 篠田 正人; 嶽村 智子, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Nara Women's University, 3380000, 2600000, 780000


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