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
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