Researchers Database

TAKEMURA Tomoko

FacultyFaculty Division of Natural Sciences Research Group of Mathematics
PositionAssociate Professor
Last Updated :2024/02/22

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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
  • Refereed, Annual Reports of Graduate School of Humanities and Science, Feller property and Dirichlet forms for skew product diffusion processes and their time change, TAKEMURA, Tomoko; TOMISAKI, Matsuyo, Mar. 2023, 38, 85, 95
  • 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
  • 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, Scientific journal, 10.3792/pjaa.91.9
  • 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
  • RIMS Kokyuroku, Kyoto University, Levy measure density corresponding to inverse local time (Probability Symposium), Tomisaki Matsuyo; Takemura Tomoko, Oct. 2013, 1855, 23, 27
  • 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, Scientific journal, 10.4171/PRIMS/113
  • 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, Scientific journal, 10.1007/s11118-011-9262-9
  • 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, Scientific journal, 10.2206/kyushujm.66.171
  • 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, Scientific journal, 10.3792/pjaa.87.119
  • 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, 10.18910/5745
  • 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

MISC

  • Refereed, 数学セミナー, 『私の科学者ライフ』, Tomoko TAKEMURA, Jan. 2023, Book review
  • 数学通信, 女性数学者交流会「女性だれでも懇談会」の紹介, 佐々田 槙子; 嶽村 智子, 2022, 26, 4, 42, 48, Introduction other

Books etc

  • めくるめく数学。 : 女性数学者たちが語るうるわしき数学の物語, 明日香出版社, 嶽村, 智子; 大山口, 菜都美; 酒井, 祐貴子, Sep. 2023, 269p, 9784756922885

Presentations

  • Oral presentation, 17 Feb. 2023, 19 Feb. 2023
  • 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
  • Tomoko TAKEMURA, 研究集会「マルコフ過程とその周辺」, 境界条件を伴うチューブ内を運動する拡散過程の収束定理, 19 Feb. 2023, 17 Feb. 2023, 19 Feb. 2023

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

  • 07 Sep. 2022, 09 Sep. 2022, Coinvestigator
  • 01 Apr. 2022, 31 Mar. 2027, 22K03353, Principal investigator
  • 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;kaken
  • 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;kaken
  • 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。, kaken
  • 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, 本研究では、人々が楽しめる様々なゲームにおいてプレイヤーが「勝利する」または「期待利得を最大にする」ためのベストな戦略を数学的に考察して厳密に解き、その解の特徴を調べることでそのゲームの持つ性質を明らかにし、実際に人々がそのゲームをプレイするときにより楽しめるようなルール設定の提案や、ゲームを一般化したときに現れる数学的に興味深い性質を追求する。さらにこうして得られた様々なゲームの理論解を用いて、この理論解との近さや解への収束の速さを調べることによって機械学習による最適化の各手法の有用性と優劣を判定する方法を提案するものである。 研究当初の2年間は様々な数理ゲームを解くことに重点を置いており、特に今年度は石取りゲームの一つであるNimの変形である一般化Delete Nim に注目した。このゲームは石を含む山の数が一定となるように山の削除と分割を繰り返すゲームであるが、この山の数を一般化した2種の発展ルールを導入し、それぞれについて研究を行った。 その結果として、All-but-One delete Nimにおいてはすべての山数に対する勝敗判定条件を、またSingle delete Nimでは4山までの勝敗判定条件を得た。この結果は3月の情報処理学会ゲーム情報学研究会で発表し、研究報告として論文公表を行った。このdelet Nimについては半数の山を削除し残りの山をそれぞれ分割するルールでのゲームの共同研究も行い、共著論文として2022年度に公表する予定である。 これらのゲームは初期状態の石数が大きいと勝敗判定方法を経験的に得ることは難しいと考えられ、今回数学的にこれらの判定条件が得られたことで機械学習の有効性の判定に活用できると考えている。, kaken
  • 基盤研究(C), Apr. 2022, Mar. 2027, 22K03353, Principal investigator, 多様な斜積拡散過程の解析とその極限定理, Tomoko TAKEMURA, 日本学術振興会, 科学研究費助成事業 基盤研究(C), 奈良女子大学, 3380000, 2600000, 780000, kaken


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