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過去の記録 ～04/22｜本日 04/23 | 今後の予定 04/24～
2007年04月05日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
Robert P. GILBERT 氏 (デラウェア大学・数学教室)
Acoustic Modeling and Osteoporotic Evaluation of Bone
Robert P. GILBERT 氏 (デラウェア大学・数学教室)
Acoustic Modeling and Osteoporotic Evaluation of Bone
[ 講演概要 ]
In this talk we discuss the modeling of the acoustic response of cancellous bone using the methods of homogenization.
This can lead to Biot type equations or more generalized equations. We develop the effective acoustic equations for cancellous bone. It is assumed that the bone matrix is elastic and the interstitial blood-marrow can be modeled as a Navier-Stokes system.
We also discuss the use of the Biot model and consider its applicability to cancellous bone. One of the questions this talk addresses is whether the clinical experiments customarily performed can be used to determine the parameters of the Biot or other bone models. A parameter recovery algorithm which uses parallel processing is developed and tested.
In this talk we discuss the modeling of the acoustic response of cancellous bone using the methods of homogenization.
This can lead to Biot type equations or more generalized equations. We develop the effective acoustic equations for cancellous bone. It is assumed that the bone matrix is elastic and the interstitial blood-marrow can be modeled as a Navier-Stokes system.
We also discuss the use of the Biot model and consider its applicability to cancellous bone. One of the questions this talk addresses is whether the clinical experiments customarily performed can be used to determine the parameters of the Biot or other bone models. A parameter recovery algorithm which uses parallel processing is developed and tested.
2007年03月26日(月)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge)
Existence of minimal models and flips (3rd talk of three)
Professor Caucher Birkar 氏 (University of Cambridge)
Existence of minimal models and flips (3rd talk of three)
2007年03月22日(木)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Matteo Novaga 氏 (Hokkaido University / Universita di Pisa)
A semidiscrete scheme for the Perona Malik equation
http://coe.math.sci.hokudai.ac.jp/
Matteo Novaga 氏 (Hokkaido University / Universita di Pisa)
A semidiscrete scheme for the Perona Malik equation
[ 講演概要 ]
We discuss the convergence of the spatial semidiscrete scheme for the one-dimensional Perona-Malik equation. If the initial datum is 1-Lipschitz out of a finite number of jump points, we haracterize the problem satisfied by the limit solution. In the general case, we construct a solution by a careful inspection of the behaviour of the approximating solutions in a space-time neighbourhood of the jump points.
[ 参考URL ]We discuss the convergence of the spatial semidiscrete scheme for the one-dimensional Perona-Malik equation. If the initial datum is 1-Lipschitz out of a finite number of jump points, we haracterize the problem satisfied by the limit solution. In the general case, we construct a solution by a careful inspection of the behaviour of the approximating solutions in a space-time neighbourhood of the jump points.
http://coe.math.sci.hokudai.ac.jp/
代数幾何学セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge)
On boundedness of log Fano varieties (2nd talk of three)
Professor Caucher Birkar 氏 (University of Cambridge)
On boundedness of log Fano varieties (2nd talk of three)
2007年03月20日(火)
代数幾何学セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge
)
Singularities and termination of flips (1st talk of three)
Professor Caucher Birkar 氏 (University of Cambridge
)
Singularities and termination of flips (1st talk of three)
2007年03月17日(土)
東京無限可積分系セミナー
13:30-14:30 数理科学研究科棟(駒場) 117号室
Paul Wiegmann 氏 (Chicago Univ.)
Calogero model and Quantum Benjamin-Ono Equation
Paul Wiegmann 氏 (Chicago Univ.)
Calogero model and Quantum Benjamin-Ono Equation
[ 講演概要 ]
TBA
TBA
2007年03月09日(金)
講演会
10:30-12:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
魅力ある大学院教育イニシアティブ特別講演会
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
[ 講演概要 ]
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
2007年03月08日(木)
講演会
15:30-17:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
魅力ある大学院教育イニシアティブ特別講演
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
[ 講演概要 ]
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
2007年03月07日(水)
諸分野のための数学研究会
14:00-15:00 数理科学研究科棟(駒場) 056号室
Seung Yeal Ha 氏 (Seoul National University)
Stability theory in L^p for the space-inhomogeneous Boltzmann equation
http://coe.math.sci.hokudai.ac.jp/index.html.en
Seung Yeal Ha 氏 (Seoul National University)
Stability theory in L^p for the space-inhomogeneous Boltzmann equation
[ 講演概要 ]
In this talk, I will present kinetic nonlinear funtionals which are similar in sprit to Glimm type functionals in one-dimensional hyperbolic conservation laws. These functionals measures the dispersive mechanism of the Boltzmann equation near vacuum and can be used to the study of the large-time behavior and L^p-stability of the Boltzmann equation near vacuum. This is a joint work with M. Yamazaki (Univ. of Tsukuba) and Seok-Bae Yun (Seoul National Univ.)
[ 参考URL ]In this talk, I will present kinetic nonlinear funtionals which are similar in sprit to Glimm type functionals in one-dimensional hyperbolic conservation laws. These functionals measures the dispersive mechanism of the Boltzmann equation near vacuum and can be used to the study of the large-time behavior and L^p-stability of the Boltzmann equation near vacuum. This is a joint work with M. Yamazaki (Univ. of Tsukuba) and Seok-Bae Yun (Seoul National Univ.)
http://coe.math.sci.hokudai.ac.jp/index.html.en
2007年02月22日(木)
講演会
10:30-12:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
※Osher先生の講演は中止になりました。
Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
魅力ある大学院教育イニシアティブ特別講演会
※Osher先生の講演は中止になりました。
Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
[ 講演概要 ]
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
講演会
13:00-15:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
[ 講演概要 ]
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
2007年02月21日(水)
講演会
10:30-12:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
※Osher先生の講演は中止になりました。
Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
魅力ある大学院教育イニシアティブ特別講演会
※Osher先生の講演は中止になりました。
Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
[ 講演概要 ]
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
講演会
13:30-15:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
[ 講演概要 ]
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
2007年02月20日(火)
講演会
10:30-17:20 数理科学研究科棟(駒場) 123号室
Erwin Bolthausen 氏 (University of Zurich) 10:30-12:00
Exit distributions for random walks in random environments
Erwin Bolthausen 氏 (University of Zurich) 14:00-15:30
Quasi one-dimensional random walks in random environments
田村要造 氏 (慶応大理工) 15:50-16:30
Large deviation principle for currents generated by stochasticline integrals
on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)
長田博文 氏 (九大数理) 16:40-17:20
Interacting Brownian motions related to Ginibre random point field
Erwin Bolthausen 氏 (University of Zurich) 10:30-12:00
Exit distributions for random walks in random environments
Erwin Bolthausen 氏 (University of Zurich) 14:00-15:30
Quasi one-dimensional random walks in random environments
田村要造 氏 (慶応大理工) 15:50-16:30
Large deviation principle for currents generated by stochasticline integrals
on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)
長田博文 氏 (九大数理) 16:40-17:20
Interacting Brownian motions related to Ginibre random point field
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 117号室
Patrick G¥'erard 氏 (パリ南大学)
On the dynamics of the Gross-Pitaevskii equation
Patrick G¥'erard 氏 (パリ南大学)
On the dynamics of the Gross-Pitaevskii equation
2007年02月17日(土)
東京無限可積分系セミナー
13:30-16:00 数理科学研究科棟(駒場) 117号室
阿部 友紀 氏 (上智理工数学) 13:30-14:30
Finite-dimensional representations of the small quantum algebras
Combinatorics of Young walls and crystal bases
阿部 友紀 氏 (上智理工数学) 13:30-14:30
Finite-dimensional representations of the small quantum algebras
[ 講演概要 ]
量子代数は定義にパラメーターを一つ含み、量子代数の表現論は、
そのパラメーターが1のべき根であるか、そうでないかによって大きく異なる。
さらに、1のべき根の場合は、Lusztig氏によって定義された「制限型量子代数」と、
De Conini-Kac氏らによって定義された「非制限型量子代数」の2種類が存在し、
それぞれ表現論が異なる。
また、制限型量子代数は、「小型量子代数(=small quantum algebra)」と
呼ばれる真部分代数を含み、その表現論は、制限型量子代数と非制限型量子代数の
どちらの表現論においても重要な役割を果たしている。
今回の講演では、主に以下の3点について説明したい:
●小型量子代数が、非制限型量子代数のある商代数と同型になることを、
有限型とループ型の場合に示す。
●A, B, C, D, G型の小型量子代数の有限次元既約表現を、
Schnizer表現の部分表現として構成する。
●A型の小型ループ量子代数のevaluation表現の性質を調べる。
Seok-Jin Kang 氏 (Seoul National University) 15:00-16:00量子代数は定義にパラメーターを一つ含み、量子代数の表現論は、
そのパラメーターが1のべき根であるか、そうでないかによって大きく異なる。
さらに、1のべき根の場合は、Lusztig氏によって定義された「制限型量子代数」と、
De Conini-Kac氏らによって定義された「非制限型量子代数」の2種類が存在し、
それぞれ表現論が異なる。
また、制限型量子代数は、「小型量子代数(=small quantum algebra)」と
呼ばれる真部分代数を含み、その表現論は、制限型量子代数と非制限型量子代数の
どちらの表現論においても重要な役割を果たしている。
今回の講演では、主に以下の3点について説明したい:
●小型量子代数が、非制限型量子代数のある商代数と同型になることを、
有限型とループ型の場合に示す。
●A, B, C, D, G型の小型量子代数の有限次元既約表現を、
Schnizer表現の部分表現として構成する。
●A型の小型ループ量子代数のevaluation表現の性質を調べる。
Combinatorics of Young walls and crystal bases
[ 講演概要 ]
We introduce combinatorics of Young walls and give a realization of crystal bases in terms of reduced Young walls. We also discuss their connection with representation theory of Hecke algebras.
We introduce combinatorics of Young walls and give a realization of crystal bases in terms of reduced Young walls. We also discuss their connection with representation theory of Hecke algebras.
2007年02月16日(金)
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:00～16:30(コモンルーム)
松本幸夫 氏 (東京大学・大学院数理科学研究科)
トポロジーと私の思い出
お茶&Coffee&お菓子: 16:00～16:30(コモンルーム)
松本幸夫 氏 (東京大学・大学院数理科学研究科)
トポロジーと私の思い出
[ 講演概要 ]
大学院に入ったのが1967年ですから、ちょうど40年前の
ことになります。それから「多様体のトポロジー」の分野で研究を
してきましたが、この40年間にトポロジーもずいぶん変化した
ように思います。自分の思い出話を交えて、その変化の様子をお話
できればと思います。私的な観点のものですので、それほど大所
高所からの話ではありません。
大学院に入ったのが1967年ですから、ちょうど40年前の
ことになります。それから「多様体のトポロジー」の分野で研究を
してきましたが、この40年間にトポロジーもずいぶん変化した
ように思います。自分の思い出話を交えて、その変化の様子をお話
できればと思います。私的な観点のものですので、それほど大所
高所からの話ではありません。
応用解析セミナー
15:00-16:00 数理科学研究科棟(駒場) 056号室
* 曜日と時間が普段と異なりますのでご注意ください.
Ratnasingham SHIVAJI 氏 (ミシシッピ州立大学)
Multiple positive solutions for classes of elliptic systems with combined nonlinear effects
* 曜日と時間が普段と異なりますのでご注意ください.
Ratnasingham SHIVAJI 氏 (ミシシッピ州立大学)
Multiple positive solutions for classes of elliptic systems with combined nonlinear effects
[ 講演概要 ]
We study the existence of multiple positive solutions to systems of the form
-\\Delta u = \\lambda f(v)
-\\Delta v = \\lambda g(u)
in a bounded domain in R^N under the Dirichlet boundary conditions. Here f, g belong to a class of positive functions having a combined sublinear effect at infinity. Our result also easily extends to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.
We study the existence of multiple positive solutions to systems of the form
-\\Delta u = \\lambda f(v)
-\\Delta v = \\lambda g(u)
in a bounded domain in R^N under the Dirichlet boundary conditions. Here f, g belong to a class of positive functions having a combined sublinear effect at infinity. Our result also easily extends to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.
2007年02月01日(木)
講演会
15:00-16:00 数理科学研究科棟(駒場) 118号室
連絡先:山本昌宏
Lassi Paivarinta 氏 (Helsinki University of Technology, Finland)
On Calderon's inverse conductivity problem in the plane.
連絡先:山本昌宏
Lassi Paivarinta 氏 (Helsinki University of Technology, Finland)
On Calderon's inverse conductivity problem in the plane.
講演会
16:15-17:15 数理科学研究科棟(駒場) 118号室
連絡先:山本昌宏
Nuuti Huyvonen 氏 (Helsinki University of Technology,
Finland)
Locating transparent cavities in optical absorption and scattering
tomography
連絡先:山本昌宏
Nuuti Huyvonen 氏 (Helsinki University of Technology,
Finland)
Locating transparent cavities in optical absorption and scattering
tomography
2007年01月31日(水)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 123号室
小谷正博 氏 (学習院大学)
ガラスに吸着した色素分子の一分子観察――ランダムウォークと拡散――
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
小谷正博 氏 (学習院大学)
ガラスに吸着した色素分子の一分子観察――ランダムウォークと拡散――
[ 講演概要 ]
夜空の星を望遠鏡で観察できる。星の望遠鏡観察から星の一生、ひいては宇宙の成因まで議論できる。同様に蛍光を使えば色素分子一匹を顕微鏡で見ることができる。一分子観察は個々の分子の挙動が見えるので、分子レベルでの確率的な過程を調べる手段、分子のおかれた環境の不均一を研究する手段になることが認識されてきた。
ガラスの上に希薄に吸着した蛍光性の色素を使って分子の表面拡散をしらべた。平均自乗偏位は時間に比例して増大するようにみえ、これから拡散係数を見積もることができる。
このようにして求めた拡散係数は測定環境の湿度に大きく依存することがわかった。こうして、問題はガラス表面にある数ナノメートルの吸着水のなかでの色素分子の運動の議論になってきた。拡散係数に場所ムラはあるのか、時間依存性はあるのか、実験は進行中である。
[ 参考URL ]夜空の星を望遠鏡で観察できる。星の望遠鏡観察から星の一生、ひいては宇宙の成因まで議論できる。同様に蛍光を使えば色素分子一匹を顕微鏡で見ることができる。一分子観察は個々の分子の挙動が見えるので、分子レベルでの確率的な過程を調べる手段、分子のおかれた環境の不均一を研究する手段になることが認識されてきた。
ガラスの上に希薄に吸着した蛍光性の色素を使って分子の表面拡散をしらべた。平均自乗偏位は時間に比例して増大するようにみえ、これから拡散係数を見積もることができる。
このようにして求めた拡散係数は測定環境の湿度に大きく依存することがわかった。こうして、問題はガラス表面にある数ナノメートルの吸着水のなかでの色素分子の運動の議論になってきた。拡散係数に場所ムラはあるのか、時間依存性はあるのか、実験は進行中である。
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
代数学コロキウム
15:15-18:45 数理科学研究科棟(駒場) 117号室
3講演です
Dennis Eriksson 氏 (東大数理/Paris) 15:15-16:15
Towards a proof of a metrized Deligne-Riemann-Roch theorem
小林 真一 氏 (名古屋大学多元数理) 16:30-17:30
CM楕円曲線の超特異点における2変数p進L関数
(A two variable p-adic L-function for CM elliptic curves at supersingular primes)
Frans Oort 氏 (Utrecht) 17:45-18:45
Irreducibility of strata and leaves in the moduli space of abelian varieties
3講演です
Dennis Eriksson 氏 (東大数理/Paris) 15:15-16:15
Towards a proof of a metrized Deligne-Riemann-Roch theorem
小林 真一 氏 (名古屋大学多元数理) 16:30-17:30
CM楕円曲線の超特異点における2変数p進L関数
(A two variable p-adic L-function for CM elliptic curves at supersingular primes)
Frans Oort 氏 (Utrecht) 17:45-18:45
Irreducibility of strata and leaves in the moduli space of abelian varieties
講演会
16:30-18:00 数理科学研究科棟(駒場) 126号室
Li Daqian 氏 (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems
Li Daqian 氏 (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 128号室
西山 慶彦 氏 (京都大学経済研究所)
A Sequential Unit Root Test
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/18.html
西山 慶彦 氏 (京都大学経済研究所)
A Sequential Unit Root Test
[ 講演概要 ]
It is well known that conventional unit root tests such as Dickey=Fuller and its variants do not have good power properties when sample size is not large. Lai and Siegmund (1983, AS) proved that OLS estimator of the AR(1) coefficient is asymptotically normally distributed in a sequential framework even if the time series has a unit root unlike the OLS estimator under a standard sampling scheme. We pursue this direction to propose a unit root test under a sequential sampling. The proposed test uses not only the OLS estimator of the AR(1) coefficient, which is asymptotically normal, but also the stopping time to construct the critical region, anticipating a better power property. We obtain analytic expressions of the joint distribution of the two statistics as well as its marginals under the null. We also consider the distribution of the statistics under local alternatives. The properties of the stopping time, to the best of our knowledge, have not been studied in the unit root literature. We calculate its expectation and variance.
[ 参考URL ]It is well known that conventional unit root tests such as Dickey=Fuller and its variants do not have good power properties when sample size is not large. Lai and Siegmund (1983, AS) proved that OLS estimator of the AR(1) coefficient is asymptotically normally distributed in a sequential framework even if the time series has a unit root unlike the OLS estimator under a standard sampling scheme. We pursue this direction to propose a unit root test under a sequential sampling. The proposed test uses not only the OLS estimator of the AR(1) coefficient, which is asymptotically normal, but also the stopping time to construct the critical region, anticipating a better power property. We obtain analytic expressions of the joint distribution of the two statistics as well as its marginals under the null. We also consider the distribution of the statistics under local alternatives. The properties of the stopping time, to the best of our knowledge, have not been studied in the unit root literature. We calculate its expectation and variance.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/18.html
2007年01月30日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
John F. Duncan 氏 (Harvard University)
Elliptic genera and some finite groups
Tea: 16:00 - 16:30 コモンルーム
John F. Duncan 氏 (Harvard University)
Elliptic genera and some finite groups
[ 講演概要 ]
Recent developments in the representation theory of sporadic groups
suggest new formulations of `moonshine' in which Jacobi forms take on the
role played by modular forms in the monstrous case. On the other hand,
Jacobi forms arise naturally in the study of elliptic genera. We review
the use of vertex algebra as a tool for constructing the elliptic genus of
a suitable vector bundle, and illustrate connections between this and
vertex algebraic representations of certain sporadic simple groups.
Recent developments in the representation theory of sporadic groups
suggest new formulations of `moonshine' in which Jacobi forms take on the
role played by modular forms in the monstrous case. On the other hand,
Jacobi forms arise naturally in the study of elliptic genera. We review
the use of vertex algebra as a tool for constructing the elliptic genus of
a suitable vector bundle, and illustrate connections between this and
vertex algebraic representations of certain sporadic simple groups.
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