# zbMATH — the first resource for mathematics

## Shiga, Tokuzo

Compute Distance To:
 Author ID: shiga.tokuzo Published as: Shiga, T.; Shiga, Tokuza; Shiga, Tokuzo External Links: Wikidata
 Documents Indexed: 51 Publications since 1968
all top 5

#### Co-Authors

 22 single-authored 4 Li, Zenghu 3 Ethier, Stewart N. 3 Shimizu, Akinobu 2 Comets, Francis M. 2 Greven, Andreas 2 Soshi, Takahiro 2 Tanaka, Hiroshi L. 2 Yoshida, Nobuo 1 Cox, J. Theodore 1 Cox, John Ted 1 Furuoya, Tasuku 1 Higuchi, Yasunari 1 Manabe, Shojiro 1 Nakao, Shintaro 1 Notohara, Morihiro 1 Seno, Shoichiro 1 Takahashi, Yoichiro 1 Tomisaki, Matsuyo 1 Uchiyama, Kôhei 1 Watanabe, Shinzo 1 Watanabe, Takesi 1 Yao, Lihua
all top 5

#### Serials

 14 Journal of Mathematics of Kyoto University 4 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4 Probability Theory and Related Fields 3 Osaka Journal of Mathematics 3 RIMS Kokyuroku 2 Advances in Applied Probability 1 Journal of Mathematical Biology 1 Canadian Journal of Mathematics 1 Journal of the Mathematical Society of Japan 1 Mathematische Nachrichten 1 Nagoya Mathematical Journal 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Stochastic Processes and their Applications 1 Electronic Journal of Probability 1 Electronic Communications in Probability 1 Bernoulli
all top 5

#### Fields

 47 Probability theory and stochastic processes (60-XX) 16 Biology and other natural sciences (92-XX) 3 Ordinary differential equations (34-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Measure and integration (28-XX) 1 Partial differential equations (35-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH

41 Publications have been cited 678 times in 522 Documents Cited by Year
Stochastic partial differential equations for some measure-valued diffusions. Zbl 0631.60058
Konno, Norio; Shiga, T.
1988
Bessel diffusions as an one-parameter family of diffusion processes. Zbl 0327.60047
Shiga, Tokuzo; Watanabe, Shinzo
1973
Probabilistic analysis of directed polymers in a random environment: a review. Zbl 1114.82017
Comets, Francis; Shiga, Tokuzo; Yoshida, Nobuo
2004
Two contrasting properties of solutions for one-dimensional stochastic partial differential equations. Zbl 0801.60050
Shiga, Tokuzo
1994
Directed polymers in a random environment: Path localization and strong disorder. Zbl 1042.60069
Comets, Francis; Shiga, Tokuza; Yoshida, Nobuo
2003
Infinite dimensional stochastic differential equations and their applications. Zbl 0462.60061
Shiga, Tokuzo; Shimizu, Akinobu
1980
Central limit theorem for a system of Markovian particles with mean field interactions. Zbl 0607.60095
Shiga, Tokuzo; Tanaka, Hiroshi
1985
Lyapunov exponents for the parabolic Anderson model. Zbl 1046.60057
Cranston, M.; Mountford, T. S.; Shiga, T.
2002
Stepping stone models in population genetics and population dynamics. Zbl 0656.92006
Shiga, Tokuzo
1988
Stationary states and their stability of the stepping stone model involving mutation and selection. Zbl 0642.92008
Shiga, Tokuzo; Uchiyama, Kohei
1986
Diffusion processes in population genetics. Zbl 0455.92005
Shiga, Tokuzo
1981
A recurrence criterion for Markov processes of Ornstein-Uhlenbeck type. Zbl 0677.60088
Shiga, Tokuzo
1990
Measure-valued branching diffusions: Immigrations, excursions and limit theorems. Zbl 0836.60091
Li, Zenghu; Shiga, Tokuzo
1995
Ergodic theorems and exponential decay of sample paths for certain interacting diffusion systems. Zbl 0780.60104
Shiga, Tokuzo
1992
An interacting system in population genetics. Zbl 0456.92014
Shiga, Tokuzo
1980
Lyapunov exponent for the parabolic Anderson model with Lévy noise. Zbl 1082.60057
Cranston, M.; Mountford, T. S.; Shiga, T.
2005
A stochastic equation based on a Poisson system for a class of measure- valued diffusion processes. Zbl 0751.60044
Shiga, Tokuzo
1990
A remark on infinite-dimensional Wiener processes with interactions. Zbl 0407.60098
Shiga, Tokuzo
1979
An interacting system in population genetics. I. Zbl 0494.92012
Shiga, Tokuzo
1980
Some results on Markov processes of infinite lattice spin systems. Zbl 0369.60117
Higuchi, Yasunari; Shiga, Tokuzo
1975
Exponential decay rate of survival probability in a disastrous random environment. Zbl 0884.60093
Shiga, Tokuzo
1997
Finite and infinite systems of interacting diffusions. Zbl 0836.60106
Cox, J. T.; Greven, Andreas; Shiga, Tokuzo
1995
Some problems related to Gibbs states, canonical Gibbs states and Markovian time evolutions. Zbl 0384.60075
Shiga, Tokuzo
1977
Sample Lyapunov exponent for a class of linear Markovian systems over $$\mathbb{Z}^d$$. Zbl 0908.60063
Furuoya, Tasuku; Shiga, Tokuzo
1998
Continuous time multi-allelic stepping stone models in population genetics. Zbl 0539.92012
Shiga, Tokuzo
1982
An interacting system in population genetics. II. Zbl 0494.92013
Shiga, Tokuzo
1980
Ergodic properties of the equilibrium process associated with infinitely many Markovian particles. Zbl 0361.60091
Shiga, Tokuzo; Takahashi, Yoichiro
1974
On one-dimensional stochastic differential equations with non-sticky boundary conditions. Zbl 0276.60061
Manabe, Shojiro; Shiga, Tokuzo
1973
Wandering phenomena in infinite-allelic diffusion models. Zbl 0489.60085
Shiga, Tokuzo
1982
Convergence to genetically uniform state in stepping stone models of population genetics. Zbl 0463.92011
Notohara, Morihiro; Shiga, Tokuzo
1980
A reversibility problem for Fleming-Viot processes. Zbl 0926.60043
Li, Zenghu; Shiga, Tokuzo; Yao, Lihua
1999
A certain class of infinite dimensional diffusion processes arising in population genetics. Zbl 0625.60095
Shiga, Tokuzo
1987
Diffusion models of temporally varying selection in population genetics. Zbl 0543.92012
Seno, Shoichiro; Shiga, Tokuzo
1984
On the uniqueness of solutions of stochastic differential equations with boundary conditions. Zbl 0254.60035
Nakao, Shintaro; Shiga, Tokuzo
1972
On Markov chains similar to the reflecting barrier Brownian motion. Zbl 0301.60044
Shiga, Tokuzo; Watanabe, Takesi
1968
Infinitely divisible random probability distributions with an application to a random motion in a random environment. Zbl 1127.60051
Shiga, Tokuzo; Tanaka, Hiroshi
2006
Existence and uniqueness of solutions for a class of nonlinear diffusion equations. Zbl 0648.35047
Shiga, Tokuzo
1987
A conditional limit theorem for generalized diffusion processes. Zbl 1061.60080
Li, Zenghu; Shiga, Tokuzo; Tomisaki, Matsuyo
2003
A Fleming-Viot process with unbounded selection. Zbl 0979.92028
Ethier, Stewart N.; Shiga, Tokuzo
2000
Some properties of solutions for one-dimensional SPDE’s associated with space-time white noise. Zbl 0816.60059
Shiga, Tokuzo
1991
Neutral allelic genealogy. Zbl 0806.92013
Ethier, S. N.; Shiga, Tokuzo
1994
Infinitely divisible random probability distributions with an application to a random motion in a random environment. Zbl 1127.60051
Shiga, Tokuzo; Tanaka, Hiroshi
2006
Lyapunov exponent for the parabolic Anderson model with Lévy noise. Zbl 1082.60057
Cranston, M.; Mountford, T. S.; Shiga, T.
2005
Probabilistic analysis of directed polymers in a random environment: a review. Zbl 1114.82017
Comets, Francis; Shiga, Tokuzo; Yoshida, Nobuo
2004
Directed polymers in a random environment: Path localization and strong disorder. Zbl 1042.60069
Comets, Francis; Shiga, Tokuza; Yoshida, Nobuo
2003
A conditional limit theorem for generalized diffusion processes. Zbl 1061.60080
Li, Zenghu; Shiga, Tokuzo; Tomisaki, Matsuyo
2003
Lyapunov exponents for the parabolic Anderson model. Zbl 1046.60057
Cranston, M.; Mountford, T. S.; Shiga, T.
2002
A Fleming-Viot process with unbounded selection. Zbl 0979.92028
Ethier, Stewart N.; Shiga, Tokuzo
2000
A reversibility problem for Fleming-Viot processes. Zbl 0926.60043
Li, Zenghu; Shiga, Tokuzo; Yao, Lihua
1999
Sample Lyapunov exponent for a class of linear Markovian systems over $$\mathbb{Z}^d$$. Zbl 0908.60063
Furuoya, Tasuku; Shiga, Tokuzo
1998
Exponential decay rate of survival probability in a disastrous random environment. Zbl 0884.60093
Shiga, Tokuzo
1997
Measure-valued branching diffusions: Immigrations, excursions and limit theorems. Zbl 0836.60091
Li, Zenghu; Shiga, Tokuzo
1995
Finite and infinite systems of interacting diffusions. Zbl 0836.60106
Cox, J. T.; Greven, Andreas; Shiga, Tokuzo
1995
Two contrasting properties of solutions for one-dimensional stochastic partial differential equations. Zbl 0801.60050
Shiga, Tokuzo
1994
Neutral allelic genealogy. Zbl 0806.92013
Ethier, S. N.; Shiga, Tokuzo
1994
Ergodic theorems and exponential decay of sample paths for certain interacting diffusion systems. Zbl 0780.60104
Shiga, Tokuzo
1992
Some properties of solutions for one-dimensional SPDE’s associated with space-time white noise. Zbl 0816.60059
Shiga, Tokuzo
1991
A recurrence criterion for Markov processes of Ornstein-Uhlenbeck type. Zbl 0677.60088
Shiga, Tokuzo
1990
A stochastic equation based on a Poisson system for a class of measure- valued diffusion processes. Zbl 0751.60044
Shiga, Tokuzo
1990
Stochastic partial differential equations for some measure-valued diffusions. Zbl 0631.60058
Konno, Norio; Shiga, T.
1988
Stepping stone models in population genetics and population dynamics. Zbl 0656.92006
Shiga, Tokuzo
1988
A certain class of infinite dimensional diffusion processes arising in population genetics. Zbl 0625.60095
Shiga, Tokuzo
1987
Existence and uniqueness of solutions for a class of nonlinear diffusion equations. Zbl 0648.35047
Shiga, Tokuzo
1987
Stationary states and their stability of the stepping stone model involving mutation and selection. Zbl 0642.92008
Shiga, Tokuzo; Uchiyama, Kohei
1986
Central limit theorem for a system of Markovian particles with mean field interactions. Zbl 0607.60095
Shiga, Tokuzo; Tanaka, Hiroshi
1985
Diffusion models of temporally varying selection in population genetics. Zbl 0543.92012
Seno, Shoichiro; Shiga, Tokuzo
1984
Continuous time multi-allelic stepping stone models in population genetics. Zbl 0539.92012
Shiga, Tokuzo
1982
Wandering phenomena in infinite-allelic diffusion models. Zbl 0489.60085
Shiga, Tokuzo
1982
Diffusion processes in population genetics. Zbl 0455.92005
Shiga, Tokuzo
1981
Infinite dimensional stochastic differential equations and their applications. Zbl 0462.60061
Shiga, Tokuzo; Shimizu, Akinobu
1980
An interacting system in population genetics. Zbl 0456.92014
Shiga, Tokuzo
1980
An interacting system in population genetics. I. Zbl 0494.92012
Shiga, Tokuzo
1980
An interacting system in population genetics. II. Zbl 0494.92013
Shiga, Tokuzo
1980
Convergence to genetically uniform state in stepping stone models of population genetics. Zbl 0463.92011
Notohara, Morihiro; Shiga, Tokuzo
1980
A remark on infinite-dimensional Wiener processes with interactions. Zbl 0407.60098
Shiga, Tokuzo
1979
Some problems related to Gibbs states, canonical Gibbs states and Markovian time evolutions. Zbl 0384.60075
Shiga, Tokuzo
1977
Some results on Markov processes of infinite lattice spin systems. Zbl 0369.60117
Higuchi, Yasunari; Shiga, Tokuzo
1975
Ergodic properties of the equilibrium process associated with infinitely many Markovian particles. Zbl 0361.60091
Shiga, Tokuzo; Takahashi, Yoichiro
1974
Bessel diffusions as an one-parameter family of diffusion processes. Zbl 0327.60047
Shiga, Tokuzo; Watanabe, Shinzo
1973
On one-dimensional stochastic differential equations with non-sticky boundary conditions. Zbl 0276.60061
Manabe, Shojiro; Shiga, Tokuzo
1973
On the uniqueness of solutions of stochastic differential equations with boundary conditions. Zbl 0254.60035
Nakao, Shintaro; Shiga, Tokuzo
1972
On Markov chains similar to the reflecting barrier Brownian motion. Zbl 0301.60044
Shiga, Tokuzo; Watanabe, Takesi
1968
all top 5

#### Cited by 543 Authors

 15 Fleischmann, Klaus 15 Li, Zenghu 14 Dawson, Donald Andrew 13 Müller, Carl E. 13 Mytnik, Leonid 11 Comets, Francis M. 11 Greven, Andreas 11 Xiong, Jie 9 Khoshnevisan, Davar 9 Perkins, Edwin A. 9 Yoshida, Nobuo 8 Cranston, Michael Craig 8 Klenke, Achim 8 Röckner, Michael 7 Etheridge, Alison Mary 7 Mountford, Thomas S. 7 Rassoul-Agha, Firas 7 Seppäläinen, Timo 6 Burdzy, Krzysztof 6 Kondrat’yev, Yuriĭ Grygorovych 6 Osada, Hirofumi 6 Quastel, Jeremy 6 Shiga, Tokuzo 6 Yor, Marc 5 Albeverio, Sergio A. 5 Cox, J. Theodore 5 den Hollander, Frank 5 Ethier, Stewart N. 5 Georgiou, Nicos 5 Graham, Carl 5 Kurtz, Thomas Gordon 5 Lacoin, Hubert 5 Méléard, Sylvie 5 Pitman, Jim William 5 Wakolbinger, Anton 5 Xi, Fubao 5 Xie, Bin 5 Zhou, Xiaowen 5 Zygouras, Nikolaos 4 Blath, Jochen 4 Corwin, Ivan 4 da Silva, Telles Timóteo 4 Del Moral, Pierre 4 Feng, Shui 4 Foondun, Mohammud 4 Fragoso, Marcelo Dutra 4 Hong, Wenming 4 Hu, Yueyun 4 Nakashima, Makoto 4 Notohara, Morihiro 4 Roelly, Sylvie 4 Sun, Rongfeng 4 Tribe, Roger P. 4 Yang, Xu 3 Alberts, Tom 3 Bates, Erik 3 Blount, Douglas 3 Bo, Lijun 3 Budhiraja, Amarjit S. 3 Caravenna, Francesco 3 Carmona, Philippe 3 Chatterjee, Sourav 3 Chen, Le 3 Dalang, Robert C. 3 Döring, Leif 3 Evans, Steven Neil 3 Handa, Kenji 3 He, Hui 3 Hutzenthaler, Martin 3 Iizuka, Masaru 3 Kawabi, Hiroshi 3 Khanin, Konstantin M. 3 Kim, Kunwoo 3 Lalley, Steven P. 3 Ma, Chunhua 3 Mano, Shuhei 3 Moreno, Gregorio 3 Ohkubo, Jun 3 Pfaffelhuber, Peter 3 Shao, Jinghai 3 Spohn, Herbert 3 Swart, Jan M. 3 Tindel, Samy 3 Viens, Frederi G. 3 Wang, Hao 3 Wang, Yongjin 3 Wu, Ruoyu 3 Yamamuro, Kouji 3 Yamazato, Makoto 3 Yilmaz, Atilla 3 Zambotti, Lorenzo 2 Alili, Larbi 2 Athreya, Siva R. 2 Baake, Ellen 2 Bai, Xiaoming 2 Barton, Nick H. 2 Borodin, Alexei 2 Chen, Xia 2 Chen, Yu-Ting 2 Chong, Carsten ...and 443 more Authors
all top 5

#### Cited in 113 Serials

 61 Stochastic Processes and their Applications 60 The Annals of Probability 53 Probability Theory and Related Fields 26 The Annals of Applied Probability 24 Journal of Statistical Physics 16 Communications in Mathematical Physics 16 Statistics & Probability Letters 15 Journal of Theoretical Probability 14 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 13 Theoretical Population Biology 9 Journal of Mathematical Biology 8 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 8 Electronic Journal of Probability 7 Journal of Applied Probability 7 Journal of Functional Analysis 7 Infinite Dimensional Analysis, Quantum Probability and Related Topics 6 Journal of Mathematical Analysis and Applications 5 Journal of Differential Equations 5 Transactions of the American Mathematical Society 5 Stochastic Analysis and Applications 5 Acta Applicandae Mathematicae 5 Bulletin des Sciences Mathématiques 5 Bernoulli 4 Journal of Multivariate Analysis 4 Science in China. Series A 4 Electronic Communications in Probability 4 Stochastic and Partial Differential Equations. Analysis and Computations 3 Discrete and Continuous Dynamical Systems 3 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 3 Journal of Statistical Mechanics: Theory and Experiment 3 Frontiers of Mathematics in China 3 Journal of Physics A: Mathematical and Theoretical 2 Advances in Applied Probability 2 Communications on Pure and Applied Mathematics 2 Israel Journal of Mathematics 2 Journal of Mathematical Physics 2 Letters in Mathematical Physics 2 Lithuanian Mathematical Journal 2 Stochastics 2 Reviews in Mathematical Physics 2 Applied Mathematics and Optimization 2 Illinois Journal of Mathematics 2 Inventiones Mathematicae 2 Journal of the Mathematical Society of Japan 2 Journal of Soviet Mathematics 2 Kodai Mathematical Journal 2 Mathematische Nachrichten 2 Nagoya Mathematical Journal 2 Osaka Journal of Mathematics 2 Proceedings of the American Mathematical Society 2 Chinese Science Bulletin 2 Journal of Dynamics and Differential Equations 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 NoDEA. Nonlinear Differential Equations and Applications 2 Mathematical Finance 2 International Journal of Theoretical and Applied Finance 2 Acta Mathematica Sinica. English Series 2 Stochastics 2 Science China. Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of the Franklin Institute 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nonlinearity 1 Periodica Mathematica Hungarica 1 Physica A 1 Transport Theory and Statistical Physics 1 Mathematics of Computation 1 Chaos, Solitons and Fractals 1 Theory of Probability and its Applications 1 Acta Mathematica Vietnamica 1 The Annals of Statistics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Mathematische Annalen 1 Mathematics and Computers in Simulation 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the Japan Academy. Series A 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Quarterly of Applied Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 Advances in Applied Mathematics 1 Mathematical Social Sciences 1 Insurance Mathematics & Economics 1 Chinese Annals of Mathematics. Series B 1 Social Choice and Welfare 1 Revista Matemática Iberoamericana 1 Forum Mathematicum 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Indagationes Mathematicae. New Series 1 Potential Analysis 1 Theory of Probability and Mathematical Statistics 1 Journal of Mathematical Sciences (New York) 1 Journal of the European Mathematical Society (JEMS) 1 Methodology and Computing in Applied Probability 1 Brazilian Journal of Probability and Statistics 1 The ANZIAM Journal 1 Nonlinear Analysis. Real World Applications ...and 13 more Serials
all top 5

#### Cited in 28 Fields

 489 Probability theory and stochastic processes (60-XX) 124 Statistical mechanics, structure of matter (82-XX) 63 Partial differential equations (35-XX) 53 Biology and other natural sciences (92-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Operator theory (47-XX) 12 Global analysis, analysis on manifolds (58-XX) 10 Statistics (62-XX) 8 Combinatorics (05-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Systems theory; control (93-XX) 7 Potential theory (31-XX) 7 Ordinary differential equations (34-XX) 7 Quantum theory (81-XX) 6 Functional analysis (46-XX) 6 Numerical analysis (65-XX) 5 Measure and integration (28-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Real functions (26-XX) 3 Operations research, mathematical programming (90-XX) 2 Number theory (11-XX) 2 Special functions (33-XX) 2 Fluid mechanics (76-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Information and communication theory, circuits (94-XX)

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.