Ken-iti Sato

Professor Emeritus, Nagoya University
Doctor of Science (Mathematics) (University of Tokyo)

K. Sato, when abbreviated (about my name)

Hachiman-yama, Tenpaku-ku, Nagoya, Japan

Research interest

  • Lévy processes, additive processes, and infinitely divisible distributions
  • Ornstein-Uhlenbeck type processes, selfsimilar additive processes, and selfdecomposable distributions
  • Stochastic integrals with respect to additive processes
  • Lévy processes and convolution semigroups with parameter in a cone

Recently Added Material in This Page

Preprints

Mathematical Papers

2018

    1. A. Lindner, Lei Pan, K. Sato (2018) On quasi-infinitely divisible distributions, Trans. Amer. Math. Soc, 370, 8483-8520.. https://arxiv.org/abs/1701.02400

2014

     1. K. Sato (2014) Stochastic integrals with respect to Lévy processes and infinitely divisible distributions, Sugaku Expositions, 27, 19-42 (PDF)

2013

  1. M. Maejima, V. Pérez-Abreu, K. Sato (2013) Lévy meaures involving a generalized form of fractional integrals, Probab. Math. Statist, 33, Fasc. 1, 45-63 (PDF)
  2. K. Sato, Y. Ueda (2013) Weak drifts of infinitely divisible distributions and their applications, J. Theoretical Probability, 26, 885-898. http://arxiv.org/abs/1204.1866
  3. K. Sato (2013) Inversions of infinitely divisible distributions and conjugates of stochastic integral mappings, J. Theoretical Probability, 26, 901-931. http://arxiv.org/abs/1204.1861

2012

  1. M. Maejima, V. Pérez-Abreu, K. Sato (2012) A class of multivariate infinitely divisible distributions related to arcsine density, Bernoulli, Vol. 18, No. 2, 476-495. http://arxiv.org/abs/1205.1654

2011

  1. K. Sato (2011) Description of limits of ranges of iterations of stochastic integral mappings of infinitely divisible distributions, ALEA Latin American Journal of Probability and Mathematical Statistics, 8, 1-17. http://alea.impa.br/english/
  2. K. Sato (2011) Stochastic integrals with respect to Lévy processes and infinitely divisible distributions, Sûgaku, 63, No. 2, 17-37 (in Japanese).
  3. A. Lindner, K. Sato (2011) Properties of stationary distributions of a sequence of generalized Ornstein-Uhlenbeck processes, Math. Nachr., 284, 2225-2248. (PDF)

2010

  1. K. Sato (2010) Fractional integrals and extensions of selfdecomposability, Lecture Notes in Math. (Springer), 2001, Lévy Matters I, 1-91. (PDF of manuscript)

2009

  1. A. Lindner, K. Sato (2009) Continuity properties and infinite divisibility of stationary distributions of some generalized Ornstein-Uhlenbeck processes, Ann. Probab., 37, 250-274. (PDF)
  2. M. Maejima, K. Sato (2009) The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions, Probab. Theory Related Fields, 145, 119-142. http://arxiv.org/abs/0712.0206
  3. K. Sato (2009) Selfdecomposability and semi-selfdecomposability in subordination of cone-parameter convolution semigroups, Tokyo J. Math., 32, 81-90. (PDF of preprint)

2007

  1. K. Sato (2007) Transformations of infinitely divisible distributions via improper stochastic integrals, ALEA Latin American Journal of Probability and Mathematical Statistics, 3, 67-110. http://alea.impa.br/english/

2006

  1. O. E. Barndorff-Nielsen, M. Maejima, K. Sato (2006) Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations, Bernoulli, 12, 1-33. (PDF of preprint)
  2. K. Sato (2006) Two families of improper stochastic integrals with respect to Lévy processes, ALEA Latin American Journal of Probability and Mathematical Statistics, 1, 47-87. http://alea.impa.br/english/ Corrigenda. (PDF)
  3. K. Sato (2006) Additive processes and stochastic integrals, Illinois J. Math., 50 (Doob Volume), 825-851. http://www.math.uiuc.edu/ijm/doob/
  4. K. Sato (2006) Monotonicity and non-monotonicity of domains of stochastic integral operators, Probab. Math. Statist. 26, 23-39. (PDF of preprint)
  5. O. E. Barndorff-Nielsen, M. Maejima, K. Sato (2006) Infinite divisibility for stochastic processes and time change, J. Theoretical Probability., 19, 411-446. (PDF of preprint)
  6. H. Kondo, M. Maejima, K. Sato (2006) Some properties of exponential integrals of Lévy processes and examples, Electronic Comm. Probab., 11, 291-303. http://www.math.washington.edu/~ejpecp/ECP/index.php (PDF of preprint)

2005

  1. J. Pedersen, K. Sato (2005) The class of distributions of periodic Ornstein-Uhlenbeck processes driven by Lévy processes, J. Theoretical Probability, 18, 209-235.
  2. K. Sato, T. Watanabe (2005) Last exit times for transient semistable processes, Ann. Inst. Henri Poincaré, Probab. Statist., 41, 929-951.

2004

  1. J. Pedersen, K. Sato (2004) Semigroups and processes with parameter in a cone, in: Abstract and Applied Analysis (ed. N. M. Chuong et al., World Scientific) 499-513.
  2. K. Sato (2004) Stochastic integrals in additive processes and application to semi-Lévy processes, Osaka J. Math., 41, 211-236.
  3. J. Pedersen, K. Sato (2004) Relations between cone-parameter Lévy processes and convolution semigroups, J. Math. Soc. Japan, 56, 541-559.
  4. K. Sato, T. Watanabe (2004) Moments of last exit times for Lévy processes, Ann. Inst. Henri Poincaré, Probab. Statist., 40, 207-225.

2003

  1. J. Pedersen, K. Sato (2003) Cone-parameter convolution semigroups and their subordination, Tokyo J. Math., 26, 503-525.
  2. M. Maejima, K. Sato (2003) Semi-Lévy processes, semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlenbeck type processes, J. Math. Kyoto Univ., 43, 609-639.

2001

  1. O. E. Barndorff-Nielsen, J. Pedersen, K. Sato (2001) Multivariate subordination, self-decomposability and stability, Adv. Appl. Probab., 33, 160-187.
  2. K. Sato (2001) Subordination and self-decomposability, Stat. Probab. Letters, 54, 317-324.
  3. K. Sato (2001) Basic results on Lévy processes, in: Lévy Processes. Theory and Appliccations (ed. O. E. Barndorff-Nielsen et. al., Birkhäuser) 3-37.

2000

  1. M. Maejima, K. Sato, T. Watanabe (2000) Distributions of selfsimilar and semi-selfsimilar processes with independent increments, Stat. Probab. Letters, 47, 395-401.
  2. M. Maejima, K. Sato, T. Watanabe (2000) Completely operator semi-selfdecomposable distributions, Tokyo J. Math., 23, 235-253.
  3. K. Sato, K. Yamamuro (2000) Recurrence-transience for self-similar additive processes associated with stable distributions, Acta Applicandae Mathematicae, 63, 375-384.
List of mathematical papers 1961 - 1999

Books

  1. K. Sato (1990) Kahou Katei (additive (or Lévy) processes), Kinokuniya, Tokyo (in Japanese).
  2. K. Sato (1999) Lévy Processes and Infinitely Divisible Distributions, Cambridge Studies in Advanced Mathematics 68, Cambridge University Press. xii+486 pages. Corrections and Changes (PDF).
  3. A. Rocha-Arteaga, K. Sato (2003) Topics in Infinitely Divisible Distributions and Lévy Processes, Aportaciones Mathemáticas, Investigación 17, Sociedad Matemática Mexicana. Corrigenda (PDF).
  4. O. E. Barndorff-Nielsen, K. Sato, edited (2004) K. Itô, Stochastic Processes, Lectures Given at Aarhus University, Springer. Corrigenda (PDF).
  5. K. Sato (2013) Lévy Processes and Infinitely Divisible Distributions. Revised edition, Paperback, Cambridge Studies in Advanced Mathematics 68, Cambridge University Press. xiv+ 521 pages. ISBN 978-1-107-65649-9
  6. A. Rocha-Arteaga, K. Sato (2019) Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition. SpringerBriefs in Probability and Mathematical Statistics. viii+135 pages. ISBN 978-3-030-22699-2.
List of books (in preparation)

Lecture Notes

  1. K. Sato (1985) Lectures on Multivariate Infinitely Divisible Distributions and Operator-Stable Processes, Technical Report Series, Lab. Res. Statist. Probab. Carleton Univ. and Univ. Ottawa, No. 54, Ottawa.
  2. K. Sato (1995) Lévy Processes on the Euclidean Spaces, Lecture Notes, Institute of Mathematics, University of Zurich.
  3. K. Sato (2000) Density Transformation in Lévy Processes, MaPhySto, Aarhus, Denmark, Lecture Notes 7.
List of lecture notes and mimeographed notes (in preparation)

Selected Miscellaneous Writings

  1. K. Sato (1994) Banach lattices, potential operators, population-genetic models, L distributions, and Lévy processes (in Japanese). 14 pages. (PDF)
  2. K. Sato (2001) Lebesgue decomposition between two path space measures induced by Lévy processes, Institute of Statistical Mathematics, Cooperative Res. Rep. 137, 1-10. (PDF)
  3. K. Sato (2002) On a theorem on Lévy processes, Institute of Statistical Mathematics, Cooperative Res. Rep. 146, 33-37. (PDF)
  4. K. Sato (2005) Remarks on Pólya's theorem on characteristic functions, Institute of Statistical Mathematics, Cooperative Res. Rep. 175, 133-145. (PDF)
  5. Memo November 29, 2007, from KS. (PDF)
  6. Memo December 5, 2007, from KS. (PDF)
  7. Memo December 15, 2007, from KS. (PDF)
  8. Memo January 28, 2008, from KS. (PDF)
  9. K. Sato (2009) Comments on the book "Lévy Processes and Infinitely Divisible Distributions", I (PDF)
  10. K. Sato (2009) Distributional properties of stochastic integrals of Lévy processes -- infinite divisible or not, absolutely continuous or not, Extended abstract of special talk, March 26, 2009, Mathematical Society of Japan, 18 pages (in Japanese). (PDF)
  11. Supplement to 9, 3 pages (in Japanese). (PDF)
  12. K. Sato (translated in 2020 from the writing in 1994) Banach lattices, potential operators, population-genetic models, L distributions, and Lévy processes. (PDF)
  13. K. Sato (2020) Reminiscences, Revised version of the article that appeared in Cooperative Research Report 434 (March 2020) Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan, pp. 87-101. (PDF)
  14. K. Sato (2021) Remembering Kunita-san, Journal of Stochastic Analysis: Vol. 2 : No. 3 , Article 6.
    Available at: https://digitalcommons.lsu.edu/josa/vol2/iss3/6
List (in preparation)

Coauthors

Ole E. Barndorff-Nielsen (2001 - 06), Gyeong Suck Choi (1995 - 96), Masatoshi Fukushima (1963 - 65, 1991), Karl Gustafson (1969), Nobuyuki Ikeda (1960 - 64), Hitoshi Kondo (2006), Hiroshi Kunita (1965), Alexander Lindner (2007 - ), Makoto Maejima (1999 - 2013), Minoru Motoo (1965 - 67), Masao Nagasawa (1962 - 64), Jan Pedersen (2001 - 05), Víctor Pérez-Abreu (2008 - 2013), Alfonso Rocha-Arteaga (2001 - 03, 2017 - ), Fred W. Steutel (1998), Hiroshi Tanaka (1960 - 62), Setsuo Taniguchi (1991), Yohei Ueda (2011 - 2013), Tadashi Ueno (1960 - 65), Toshiro Watanabe (1994 - 2005), Koji Yamamuro (1996 - 98), Makoto Yamazato (1978 - 1994)

Short Biography

Born June 1934, in Tokyo
1953 - 1958: Undergraduate student, University of Tokyo
1958 - 1960: Graduate student in mathematics, University of Tokyo. Master of Science. Advisor was Kôsaku Yosida
1960 - 1965: Assistant and lecturer, Department of Mathematics, Tokyo Metropolitan University
1965: Doctor of Science, University of Tokyo
1965 - 1976: Associate professor, Tokyo University of Education. Probability group together with G. Maruyama, M. Motoo, and M. Fukushima
1976 - 1983: Associate professor and professor, Department of Mathematics, College of Liberal Arts, Kanazawa University
1983 - 1996: Professor, College of General Education and School of Informatics and Sciences, Nagoya University
1996: Professor Emeritus, Nagoya University
2008: Analysis Prize from Mathematical Society of Japan for the study of Lévy processes and infinitely divisible distributions
Visiting University of Minnesota (Aug. 1967 - Aug. 1968 and Sept. 1975-June 1976), University of Illinois (Sept. 1968 - June 1969), Carleton University (July 1981 - Apr. 1982), University of Zurich (Apr. - June 1995)
Editorship: 1982 - 1989  Member of Editorial Board, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete and Probability Theory and Related Fields
Short Courses: MaPhySto Aarhus (Jan. 2000), CIMAT Guanajuato (Jan. 2001)

Past Research Interest

Last Modified: November 14, 2021

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