## TAKEMURA TomokoFaculty Division of Natural Sciences Research Group of Mathematics Associate Professor |

Last Updated :2021/06/02

- 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

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

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

- 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

Jump measure densities corresponding to Brownian motion on an annulus

2018, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, (33), 123 - 132Exponent of inverse local time for harmonic transformed process

2016, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, 31, 127 - 138The weak mutation and strong selection limit of the Moran model satisfies the strong Markov property

2015, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, (30), 105 - 112Asymptotic behavior of Levy measure density corresponding to inverse local time

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., JAPAN ACAD, Jan. 2015, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 91 (1), 9 - 13, doi;web_of_scienceOn the convergence of weak mutation limits of the Moran model in population genetics

2014, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, (29), 131 - 140Lévy measure density corresponding to inverse local time

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, Publications of the Research Institute for Mathematical Sciences, 49 (3), 563 - 599, doiConvergence of Time Changed Skew Product Diffusion Processes

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., SPRINGER, Jan. 2013, POTENTIAL ANALYSIS, 38 (1), 31 - 55, doi;web_of_scienceh TRANSFORM OF ONE-DIMENSIONAL GENERALIZED DIFFUSION OPERATORS

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., KYUSHU UNIV, FAC MATHEMATICS, Mar. 2012, KYUSHU JOURNAL OF MATHEMATICS, 66 (1), 171 - 191, doi;web_of_scienceRecurrence/transience criteria for skew product diffusion processes

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., JAPAN ACAD, Jul. 2011, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 87 (7), 119 - 122, doi;web_of_scienceState of boundaries for harmonic transforms of one-dimensional generalized diffusion processes

2009, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, 25, 285 - 294Elementary solution of Bessel processes with boundary condition

2007, Ann. Report of Graduate School of Humanities and Sciences Nara Women's University, 23, 265 - 278

Convergence of diffusion processes in a tube

日本数学会2018年度年会, 2018Convergence for diffusions in balls whose diameter changes

KWMS International Conference 2017, 2017Convergence for diffusions in balls whose diameter changes

KWMS International Conference 2017, 2017Exponent of Levy processes corresponding to inverse local time for harmonic transformed diffusion processes

World Congress in Probability and Statistics, 2016Exponent of Levy processes corresponding to inverse local time for harmonic transformed diffusion processes

World Congress in Probability and Statistics, 2016L ́evy measure density corresponding to inverse local time

6th International Conference on Stochastic Analysis and its Applications, 2012L ́evy measure density corresponding to inverse local time

日本数学会, 2012L ́evy measure density corresponding to inverse local time

"Stochastic Analysis and Applications" German-Japanese bilateral research project, 2012L ́evy measure density corresponding to inverse local time

6th International Conference on Stochastic Analysis and its Applications, 2012L ́evy measure density corresponding to inverse local time

"Stochastic Analysis and Applications" German-Japanese bilateral research project, 2012一次元広義拡散過程のh変換

日本数学会, 2011Recurrence/transience criteria for skew product diffusion processes

5th International Conference on Stochastic Analysis and its Applications, 2011Recurrence/transience criteria for skew product diffusion processes

5th International Conference on Stochastic Analysis and its Applications, 2011Convergence of skew product diffusion processes

日本数学会, 2010斜積拡散過程の再帰性について

日本数学会, 2010h変換された一次元広義拡散過程の大域的性質

日本数学会, 2009Some property of harmonic transformed one dimensional generalized diffusion processes

First Institute of Mathematical Statistics Asia Pacific Rim Meeting, 2009Feller property and Limit theorem of skew product diffusions

33rd Conference on Stochastic Processes and Their Applications, 2009Some property of harmonic transformed one dimensional generalized diffusion processes

First Institute of Mathematical Statistics Asia Pacific Rim Meeting, 2009Feller property and Limit theorem of skew product diffusions

33rd Conference on Stochastic Processes and Their Applications, 2009一次元拡散過程とS^1上のブラウン運動の斜積について

日本数学会, 2008