## Aida, Shigeki

Compute Distance To:
 Author ID: aida.shigeki Published as: Aida, Shigeki; Aida, S. Homepage: http://www.math.tohoku.ac.jp/~aida/ External Links: MGP
 Documents Indexed: 43 Publications since 1990 Co-Authors: 12 Co-Authors with 11 Joint Publications 193 Co-Co-Authors
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### Co-Authors

 32 single-authored 2 Shigekawa, Ichiro 2 Stroock, Daniel W. 1 Driver, Bruce K. 1 Elworthy, David 1 Kawabi, Hiroshi 1 Kikuchi, Takanori 1 Kusuoka, Seiichiro Kusuoka 1 Kusuoka, Shigeo 1 Masuda, Takao 1 Naganuma, Nobuaki 1 Sasaki, Kosuke 1 Zhang, Tusheng S.
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### Serials

 15 Journal of Functional Analysis 2 Osaka Journal of Mathematics 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Stochastic Processes and their Applications 1 The Annals of Probability 1 Tôhoku Mathematical Journal. Second Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Potential Analysis 1 Mathematical Research Letters 1 Bulletin des Sciences Mathématiques 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Interdisciplinary Information Sciences (IIS) 1 RIMS Kôkyûroku Bessatsu 1 Communications on Stochastic Analysis
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### Fields

 32 Probability theory and stochastic processes (60-XX) 19 Global analysis, analysis on manifolds (58-XX) 9 Partial differential equations (35-XX) 6 Functional analysis (46-XX) 6 Quantum theory (81-XX) 3 Potential theory (31-XX) 3 Operator theory (47-XX) 2 Topological groups, Lie groups (22-XX) 2 Numerical analysis (65-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

35 Publications have been cited 458 times in 285 Documents Cited by Year
On the support of Wiener functionals. Zbl 0790.60047
Aida, S.; Kusuoka, S.; Stroock, D.
1993
Uniform positivity improving property, Sobolev inequalities, and spectral gaps. Zbl 0914.47041
Aida, Shigeki
1998
Logarithmic Sobolev inequalities and exponential integrability. Zbl 0846.46020
Aida, Shigeki; Masuda, Takao; Shigekawa, Ichiro
1994
Moment estimates derived from Poincaré and logarithmic Sobolev inequalities. Zbl 0862.60064
Aida, S.; Stroock, D.
1994
On the small time asymptotics of diffusion processes on path groups. Zbl 0993.60026
Aida, Shigeki; Zhang, Tusheng
2002
Short time asymptotics of a certain infinite dimensional diffusion process. Zbl 0976.60077
Aida, Shigeki; Kawabi, Hiroshi
2001
Differential calculus on path and loop spaces. I: Logarithmic Sobolev inequalities on path spaces. Zbl 0837.60053
Aida, Shigeki; Elworthy, David
1995
Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces. Zbl 1292.60071
Aida, Shigeki; Sasaki, Kosuke
2013
Logarithmic Sobolev inequalities and spectral gaps: Perturbation theory. Zbl 0846.46019
Aida, Shigeki; Shigekawa, Ichiro
1994
Sobolev spaces over loop groups. Zbl 0823.46034
Aida, Shigeki
1995
Differential calculus on path and loop spaces. II: Irreducibility of Dirichlet forms on loop spaces. Zbl 0937.60050
Aida, Shigeki
1998
Reflected rough differential equations. Zbl 1325.60083
Aida, Shigeki
2015
Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces. Zbl 0968.58026
Aida, Shigeki
2000
Logarithmic Sobolev inequalities on loop spaces over compact Riemannian manifolds. Zbl 0918.60041
Aida, Shigeki
1996
Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold. Zbl 1127.58014
Aida, Shigeki
2007
Semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. Zbl 1038.81027
Aida, Shigeki
2003
Equivalence of heat kernel measure and pinned Wiener measure on loop groups. Zbl 0964.22009
Aida, Shigeki; Driver, Bruce K.
2000
An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups. Zbl 1038.60077
Aida, Shigeki
2001
On the Ornstein-Uhlenbeck operators on Wiener-Riemannian manifolds. Zbl 0795.60043
Aida, Shigeki
1993
Support theorem for diffusion processes on Hilbert spaces. Zbl 0721.60064
Aida, Shigeki
1990
Vanishing of one-dimensional $$L^2$$-cohomologies of loop groups. Zbl 1236.58020
Aida, Shigeki
2011
Witten Laplacian on pinned path group and its expected semiclassical behavior. Zbl 1073.58026
Aida, Shigeki
2003
Gradient estimates of harmonic functions and the asymptotics of spectral gaps on path spaces. Zbl 0921.31007
Aida, Shigeki
1996
On the irreducibility of Dirichlet forms on domains in infinite dimensional spaces. Zbl 0981.60057
Aida, Shigeki
2000
Certain gradient flows and submanifolds in Wiener spaces. Zbl 0771.60041
Aida, Shigeki
1993
On a certain semiclassical problem on Wiener spaces. Zbl 1058.81018
Aida, Shigeki
2003
Tunneling for spatially cut-off $$P(\phi)_2$$-Hamiltonians. Zbl 1257.81027
Aida, Shigeki
2012
Precise Gaussian estimates of heat kernels on asymptotically flat Riemannian manifolds with poles. Zbl 1160.58309
Aida, Shigeki
2004
Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces. II. Zbl 1388.60115
Aida, Shigeki
2014
Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. II: $$P(\phi)_2$$-model on a finite volume. Zbl 1179.81075
Aida, Shigeki
2009
Weak Poincaré inequalities on domains defined by Brownian rough paths. Zbl 1067.60029
Aida, Shigeki
2004
Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. I: Unbounded one particle hamiltonians. Zbl 1194.81092
Aida, Shigeki
2009
Precise Gaussian lower bounds on heat kernels. Zbl 0983.35028
Aida, Shigeki
2000
$$\mathbb{D}^ \infty$$-cohomology groups and $$\mathbb{D}^ \infty$$-maps on submanifolds in Wiener spaces. Zbl 0777.60045
Aida, Shigeki
1992
COH formula and Dirichlet Laplacians on small domains of pinned path spaces. Zbl 1237.58030
Aida, Shigeki
2011
Reflected rough differential equations. Zbl 1325.60083
Aida, Shigeki
2015
Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces. II. Zbl 1388.60115
Aida, Shigeki
2014
Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces. Zbl 1292.60071
Aida, Shigeki; Sasaki, Kosuke
2013
Tunneling for spatially cut-off $$P(\phi)_2$$-Hamiltonians. Zbl 1257.81027
Aida, Shigeki
2012
Vanishing of one-dimensional $$L^2$$-cohomologies of loop groups. Zbl 1236.58020
Aida, Shigeki
2011
COH formula and Dirichlet Laplacians on small domains of pinned path spaces. Zbl 1237.58030
Aida, Shigeki
2011
Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. II: $$P(\phi)_2$$-model on a finite volume. Zbl 1179.81075
Aida, Shigeki
2009
Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. I: Unbounded one particle hamiltonians. Zbl 1194.81092
Aida, Shigeki
2009
Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold. Zbl 1127.58014
Aida, Shigeki
2007
Precise Gaussian estimates of heat kernels on asymptotically flat Riemannian manifolds with poles. Zbl 1160.58309
Aida, Shigeki
2004
Weak Poincaré inequalities on domains defined by Brownian rough paths. Zbl 1067.60029
Aida, Shigeki
2004
Semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. Zbl 1038.81027
Aida, Shigeki
2003
Witten Laplacian on pinned path group and its expected semiclassical behavior. Zbl 1073.58026
Aida, Shigeki
2003
On a certain semiclassical problem on Wiener spaces. Zbl 1058.81018
Aida, Shigeki
2003
On the small time asymptotics of diffusion processes on path groups. Zbl 0993.60026
Aida, Shigeki; Zhang, Tusheng
2002
Short time asymptotics of a certain infinite dimensional diffusion process. Zbl 0976.60077
Aida, Shigeki; Kawabi, Hiroshi
2001
An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups. Zbl 1038.60077
Aida, Shigeki
2001
Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces. Zbl 0968.58026
Aida, Shigeki
2000
Equivalence of heat kernel measure and pinned Wiener measure on loop groups. Zbl 0964.22009
Aida, Shigeki; Driver, Bruce K.
2000
On the irreducibility of Dirichlet forms on domains in infinite dimensional spaces. Zbl 0981.60057
Aida, Shigeki
2000
Precise Gaussian lower bounds on heat kernels. Zbl 0983.35028
Aida, Shigeki
2000
Uniform positivity improving property, Sobolev inequalities, and spectral gaps. Zbl 0914.47041
Aida, Shigeki
1998
Differential calculus on path and loop spaces. II: Irreducibility of Dirichlet forms on loop spaces. Zbl 0937.60050
Aida, Shigeki
1998
Logarithmic Sobolev inequalities on loop spaces over compact Riemannian manifolds. Zbl 0918.60041
Aida, Shigeki
1996
Gradient estimates of harmonic functions and the asymptotics of spectral gaps on path spaces. Zbl 0921.31007
Aida, Shigeki
1996
Differential calculus on path and loop spaces. I: Logarithmic Sobolev inequalities on path spaces. Zbl 0837.60053
Aida, Shigeki; Elworthy, David
1995
Sobolev spaces over loop groups. Zbl 0823.46034
Aida, Shigeki
1995
Logarithmic Sobolev inequalities and exponential integrability. Zbl 0846.46020
Aida, Shigeki; Masuda, Takao; Shigekawa, Ichiro
1994
Moment estimates derived from Poincaré and logarithmic Sobolev inequalities. Zbl 0862.60064
Aida, S.; Stroock, D.
1994
Logarithmic Sobolev inequalities and spectral gaps: Perturbation theory. Zbl 0846.46019
Aida, Shigeki; Shigekawa, Ichiro
1994
On the support of Wiener functionals. Zbl 0790.60047
Aida, S.; Kusuoka, S.; Stroock, D.
1993
On the Ornstein-Uhlenbeck operators on Wiener-Riemannian manifolds. Zbl 0795.60043
Aida, Shigeki
1993
Certain gradient flows and submanifolds in Wiener spaces. Zbl 0771.60041
Aida, Shigeki
1993
$$\mathbb{D}^ \infty$$-cohomology groups and $$\mathbb{D}^ \infty$$-maps on submanifolds in Wiener spaces. Zbl 0777.60045
Aida, Shigeki
1992
Support theorem for diffusion processes on Hilbert spaces. Zbl 0721.60064
Aida, Shigeki
1990
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### Cited by 281 Authors

 26 Wang, Feng-Yu 16 Aida, Shigeki 12 Bobkov, Sergey Germanovich 10 Jiang, Daqing 9 Inahama, Yuzuru 8 Röckner, Michael 8 Zhang, Tusheng S. 7 Götze, Friedrich 7 Léandre, Rémi 7 Ledoux, Michel 7 Wu, Bo 6 Friz, Peter Karl 6 Hayat, Tasawar 6 Shao, Jinghai 6 Wang, Fengyu 5 Adamczak, Radosław 5 Al-saedi, Ahmed Eid Salem 5 Cattiaux, Patrick 5 Gong, Fuzhou 5 Guillin, Arnaud 5 Li, Xue-Mei 5 Liu, Qun 5 Sanz-Solé, Marta 4 Albeverio, Sergio A. 4 Baudoin, Fabrice 4 Chen, Xin 4 Hino, Masanori 4 Lin, Yuguo 4 Liu, Wei 4 Wu, Liming 3 Bally, Vlad 3 Bogachev, Vladimir Igorevich 3 Cianchi, Andrea 3 Delgado-Vences, Francisco J. 3 Elworthy, K. David 3 Fang, Shizan 3 Gozlan, Nathael 3 Liu, Yuan 3 Pick, Luboš 3 Ren, Jiagang 3 Sambale, Holger 3 Słomiński, Leszek 3 Strzelecki, Michał 3 Sun, Xiaoxia 3 Wu, Jing 2 Bakry, Dominique 2 Barthe, Franck 2 Bonnefont, Michel 2 Brzeźniak, Zdzisław 2 Chistyakov, Gennadiy P. 2 Duerinckx, Mitia 2 Eberle, Andreas 2 Falkowski, Adrian 2 Fan, Xiliang 2 Gassiat, Paul 2 Gentil, Ivan 2 Goldys, Beniamin 2 Gordina, Maria 2 Gubinelli, Massimiliano 2 Guo, Feng 2 Hairer, Martin 2 Houdré, Christian 2 Huang, De 2 Huang, Zaitang 2 Ji, Xuehui 2 Junge, Marius 2 Kawabi, Hiroshi 2 Li, Yangrong 2 Mao, Yonghua 2 Maslowski, Bohdan 2 Musil, Vít 2 Ondreját, Martin 2 Papageorgiou, Ioannis 2 Polaczyk, Bartłomiej 2 Privault, Nicolas 2 Prömel, David J. 2 Roberto, Cyril 2 Rudnicki, Ryszard 2 Taniguchi, Setsuo 2 Tetali, Prasad 2 Thalmaier, Anton 2 Tropp, Joel A. 2 Uemura, Toshihiro 2 Wolff, Paweł 2 Xu, Lihu 2 Yang, Fenfen 2 Yang, Shuang 2 Yuan, Chenggui 2 Yuan, Sanling 2 Zeng, Qiang 2 Zhu, Huaiping 2 Zhu, RongChan 2 Zhu, Xiang-Chan 2 Zong, Gaofeng 1 Aboulalaâ, Adnan 1 Ahlberg, Daniel 1 Allan, Andrew L. 1 An, Zihao 1 Andriatahina, Jocelyn Hajaniaina 1 Aoun, Richard ...and 181 more Authors
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### Cited in 92 Serials

 47 Journal of Functional Analysis 15 The Annals of Probability 13 Stochastic Processes and their Applications 12 Potential Analysis 9 Bulletin des Sciences Mathématiques 8 Journal of Mathematical Analysis and Applications 8 Probability Theory and Related Fields 8 Journal of Theoretical Probability 8 Bernoulli 7 Physica A 7 Infinite Dimensional Analysis, Quantum Probability and Related Topics 6 Transactions of the American Mathematical Society 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Electronic Journal of Probability 5 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 4 Stochastic Analysis and Applications 4 Acta Mathematica Sinica. English Series 3 Osaka Journal of Mathematics 3 The Annals of Applied Probability 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Mathematical Physics 2 Journal of Statistical Physics 2 Journal of Geometry and Physics 2 Advances in Mathematics 2 Applied Mathematics and Computation 2 Czechoslovak Mathematical Journal 2 Mathematische Zeitschrift 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the American Mathematical Society 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Statistics & Probability Letters 2 Acta Mathematicae Applicatae Sinica. English Series 2 Forum Mathematicum 2 Science in China. Series A 2 The Journal of Geometric Analysis 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Journal of Mathematical Sciences (New York) 2 Communications in Contemporary Mathematics 2 Journal of Evolution Equations 2 Discrete and Continuous Dynamical Systems. Series B 2 Stochastics 2 ALEA. Latin American Journal of Probability and Mathematical Statistics 2 Science China. Mathematics 1 Applicable Analysis 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 Israel Journal of Mathematics 1 Journal of the Franklin Institute 1 Lithuanian Mathematical Journal 1 Mathematical Biosciences 1 Reports on Mathematical Physics 1 Mathematics of Computation 1 Reviews in Mathematical Physics 1 Acta Mathematica 1 Duke Mathematical Journal 1 Publications Mathématiques 1 Inventiones Mathematicae 1 Journal of Differential Equations 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Tôhoku Mathematical Journal. Second Series 1 Revista Matemática Iberoamericana 1 Sugaku Expositions 1 SIAM Journal on Mathematical Analysis 1 Journal of Dynamics and Differential Equations 1 Calculus of Variations and Partial Differential Equations 1 Complexity 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Discrete Dynamics in Nature and Society 1 Annales Henri Poincaré 1 Qualitative Theory of Dynamical Systems 1 Journal of Nonlinear Mathematical Physics 1 Nonlinear Analysis. Real World Applications 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Advances in Difference Equations 1 Mathematical Biosciences and Engineering 1 Oberwolfach Reports 1 Frontiers of Mathematics in China 1 Journal of Mathematical Inequalities 1 International Journal of Biomathematics 1 Confluentes Mathematici 1 Journal of Theoretical Biology 1 Forum of Mathematics, Sigma 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Advances in Mathematics. Scientific Journal 1 Journal of Function Spaces 1 Probability, Uncertainty and Quantitative Risk
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### Cited in 35 Fields

 227 Probability theory and stochastic processes (60-XX) 73 Global analysis, analysis on manifolds (58-XX) 54 Operator theory (47-XX) 44 Partial differential equations (35-XX) 32 Functional analysis (46-XX) 22 Potential theory (31-XX) 16 Biology and other natural sciences (92-XX) 15 Real functions (26-XX) 15 Measure and integration (28-XX) 14 Statistical mechanics, structure of matter (82-XX) 13 Dynamical systems and ergodic theory (37-XX) 12 Quantum theory (81-XX) 10 Differential geometry (53-XX) 8 Numerical analysis (65-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Difference and functional equations (39-XX) 5 Statistics (62-XX) 4 Topological groups, Lie groups (22-XX) 4 Ordinary differential equations (34-XX) 4 Fluid mechanics (76-XX) 4 Systems theory; control (93-XX) 3 Approximations and expansions (41-XX) 3 Integral equations (45-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Combinatorics (05-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Algebraic topology (55-XX) 1 General and overarching topics; collections (00-XX) 1 Commutative algebra (13-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX)