Keniti Sato

Professor Emeritus, Nagoya University
Doctor of Science (Mathematics) (University of Tokyo)
K. Sato, when abbreviated (about my
name)
Hachimanyama, Tenpakuku, Nagoya, Japan
Research interest
 Lévy processes, additive processes, and infinitely
divisible distributions
 OrnsteinUhlenbeck type processes, selfsimilar
additive processes, and selfdecomposable distributions
 Stochastic integrals with respect to additive processes
 Coneparameter Lévy processes and convolution semigroups

Recently Added Material in This Page
 Corrections and Changes. Lévy Processes and Infinitely Divisible
Distributions. (PDF
updated May 30, 2013)
 One book: Lévy Processes and Infinitely Divisible Distributions.
Revised edition. Paperback (November 2013) .
 One mathematical paper in 2018.
 One book: A.
RochaArteaga, K. Sato. Topics in Infinitely Divisible Distributions
and Lévy Processes, Revised Edition. (November 2019)
 One item in Selected Miscellaneous Writings: Banach lattices, potential
operators, populationgenetic models, L distributions,
and Lévy processes. (PDF)
 One item in Selected Miscellaneous Writings: Reminiscences, Revised version
of the article that appeared in Cooperative Research Report 434 (March
2020) Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan, pp.
87101. (PDF)
Preprints
 K. Sato, Additive processes and independently scattered random
measures (in preparation).
 K. Sato, Reminiscences (PDF)
Mathematical Papers
2018
1. A. Lindner, Lei Pan, K. Sato (2018) On
quasiinfinitely divisible distributions, Trans. Amer. Math. Soc, 370,
84838520.. 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, 1942 (PDF)
2013
 M. Maejima, V. PérezAbreu, K. Sato (2013) Lévy meaures
involving a generalized form of fractional integrals, Probab. Math.
Statist, 33, Fasc. 1, 4563 (PDF)
 K. Sato, Y. Ueda (2013) Weak drifts of infinitely divisible
distributions and their applications, J. Theoretical Probability, 26,
885898. http://arxiv.org/abs/1204.1866
 K. Sato (2013) Inversions of infinitely divisible distributions and
conjugates of stochastic integral mappings, J. Theoretical Probability,
26, 901931. http://arxiv.org/abs/1204.1861
2012
 M. Maejima, V. PérezAbreu, K. Sato (2012) A class of multivariate
infinitely divisible distributions related to arcsine density,
Bernoulli, Vol. 18, No. 2, 476495. http://arxiv.org/abs/1205.1654
2011
 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,
117. http://alea.impa.br/english/
 K. Sato (2011) Stochastic integrals with respect to Lévy processes and
infinitely divisible distributions, Sûgaku, 63, No. 2, 1737 (in
Japanese).
 A. Lindner, K. Sato (2011) Properties of stationary distributions of a
sequence of generalized OrnsteinUhlenbeck processes, Math. Nachr., 284,
22252248. (PDF)
2010
 K. Sato (2010) Fractional integrals and extensions of
selfdecomposability, Lecture Notes in Math. (Springer), 2001, Lévy
Matters I, 191. (PDF of
manuscript)
2009
 A. Lindner, K. Sato (2009) Continuity properties and infinite
divisibility of stationary distributions of some generalized
OrnsteinUhlenbeck processes, Ann. Probab., 37, 250274. (PDF)
 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, 119142. http://arxiv.org/abs/0712.0206
 K. Sato (2009) Selfdecomposability and semiselfdecomposability in
subordination of coneparameter convolution semigroups, Tokyo J. Math.,
32, 8190. (PDF of preprint)
2007
 K. Sato (2007) Transformations of infinitely divisible distributions
via improper stochastic integrals, ALEA Latin American Journal of
Probability and Mathematical Statistics, 3, 67110. http://alea.impa.br/english/
2006
 O. E. BarndorffNielsen, M. Maejima, K. Sato (2006) Some classes of
multivariate infinitely divisible distributions admitting stochastic
integral representations, Bernoulli, 12, 133. (PDF
of preprint)
 K. Sato (2006) Two families of improper stochastic integrals with
respect to Lévy processes, ALEA Latin American Journal of Probability
and Mathematical Statistics, 1, 4787. http://alea.impa.br/english/ Corrigenda. (PDF)
 K. Sato (2006) Additive processes and stochastic integrals, Illinois
J. Math., 50 (Doob Volume), 825851. http://www.math.uiuc.edu/ijm/doob/
 K. Sato (2006) Monotonicity and nonmonotonicity of domains of
stochastic integral operators, Probab. Math. Statist. 26, 2339. (PDF
of preprint)
 O. E. BarndorffNielsen, M. Maejima, K. Sato (2006) Infinite
divisibility for stochastic processes and time change, J. Theoretical
Probability., 19, 411446. (PDF of preprint)
 H. Kondo, M. Maejima, K. Sato (2006) Some properties of exponential
integrals of Lévy processes and examples, Electronic Comm. Probab., 11,
291303. http://www.math.washington.edu/~ejpecp/ECP/index.php
(PDF of preprint)
2005
 J. Pedersen, K. Sato (2005) The class of distributions of periodic
OrnsteinUhlenbeck processes driven by Lévy processes, J. Theoretical
Probability, 18, 209235.
 K. Sato, T. Watanabe (2005) Last exit times for transient semistable
processes, Ann. Inst. Henri Poincaré, Probab. Statist., 41, 929951.
2004
 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) 499513.
 K. Sato (2004) Stochastic integrals in additive processes and
application to semiLévy processes, Osaka J. Math., 41, 211236.
 J. Pedersen, K. Sato (2004) Relations between coneparameter Lévy
processes and convolution semigroups, J. Math. Soc. Japan, 56, 541559.
 K. Sato, T. Watanabe (2004) Moments of last exit times for Lévy
processes, Ann. Inst. Henri Poincaré, Probab. Statist., 40, 207225.
2003
 J. Pedersen, K. Sato (2003) Coneparameter convolution semigroups and
their subordination, Tokyo J. Math., 26, 503525.
 M. Maejima, K. Sato (2003) SemiLévy processes, semiselfsimilar
additive processes, and semistationary OrnsteinUhlenbeck type
processes, J. Math. Kyoto Univ., 43, 609639.
2001
 O. E. BarndorffNielsen, J. Pedersen, K. Sato (2001) Multivariate
subordination, selfdecomposability and stability, Adv. Appl. Probab.,
33, 160187.
 K. Sato (2001) Subordination and selfdecomposability, Stat. Probab.
Letters, 54, 317324.
 K. Sato (2001) Basic results on Lévy processes, in: Lévy Processes.
Theory and Appliccations (ed. O. E. BarndorffNielsen et. al.,
Birkhäuser) 337.
2000
 M. Maejima, K. Sato, T. Watanabe (2000) Distributions of selfsimilar
and semiselfsimilar processes with independent increments, Stat.
Probab. Letters, 47, 395401.
 M. Maejima, K. Sato, T. Watanabe (2000) Completely operator
semiselfdecomposable distributions, Tokyo J. Math., 23, 235253.
 K. Sato, K. Yamamuro (2000) Recurrencetransience for selfsimilar
additive processes associated with stable distributions, Acta
Applicandae Mathematicae, 63, 375384.
List of mathematical papers 1961  1999
Books
 K. Sato (1990) Kahou Katei (additive (or Lévy) processes), Kinokuniya,
Tokyo (in Japanese).
 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).
 A. RochaArteaga, K. Sato (2003) Topics in Infinitely Divisible
Distributions and Lévy Processes, Aportaciones Mathemáticas,
Investigación 17, Sociedad Matemática Mexicana. Corrigenda (PDF).
 O.
E. BarndorffNielsen, K. Sato, edited (2004) K. Itô, Stochastic
Processes, Lectures Given at Aarhus University, Springer.
Corrigenda (PDF).
 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 9781107656499
 A.
RochaArteaga, K. Sato (2019) Topics in Infinitely Divisible
Distributions and Lévy Processes, Revised Edition. SpringerBriefs in
Probability and Mathematical Statistics. viii+135 pages. ISBN
9783030226992.
List of books (in preparation)
Lecture Notes
 K. Sato (1985) Lectures on Multivariate Infinitely Divisible
Distributions and OperatorStable Processes, Technical Report Series,
Lab. Res. Statist. Probab. Carleton Univ. and Univ. Ottawa, No. 54,
Ottawa.
 K. Sato (1995) Lévy Processes on the Euclidean Spaces, Lecture Notes,
Institute of Mathematics, University of Zurich.
 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
 K. Sato (1994) Banach lattices, potential operators,
populationgenetic models, L distributions, and Lévy processes
(in Japanese). 14 pages. (PDF)
 K. Sato (2001) Lebesgue decomposition between two path space measures
induced by Lévy processes, Institute of Statistical Mathematics,
Cooperative Res. Rep. 137, 110. (PDF)
 K. Sato (2002) On a theorem on Lévy processes, Institute of
Statistical Mathematics, Cooperative Res. Rep. 146, 3337. (PDF)
 K. Sato (2005) Remarks on Pólya's theorem on characteristic functions,
Institute of Statistical Mathematics, Cooperative Res. Rep. 175,
133145. (PDF)
 Memo November 29, 2007, from KS. (PDF)
 Memo December 5, 2007, from KS. (PDF)
 Memo December 15, 2007, from KS. (PDF)
 Memo January 28, 2008, from KS. (PDF)
 K. Sato (2009) Comments on the book "Lévy Processes and Infinitely
Divisible Distributions", I (PDF)
 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)
 Supplement to 9, 3 pages (in Japanese). (PDF)
 K. Sato (translated in 2020 from the writing in 1994) Banach lattices,
potential operators, populationgenetic models, L distributions,
and Lévy processes. (PDF)
 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. 87101. (PDF)
List (in preparation)
Coauthors
Ole E.
BarndorffNielsen (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
PérezAbreu (2008  2013), Alfonso RochaArteaga (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.
1975June 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
 Markov processes. Boundary problems
 Markov processes. (Recurrent) potential operators
 Banach lattices. Abstract maximum principle
 Potential operators
 Markov chain models in population genetics
 Convergence of populationgenetical models to diffusions
Last Modified: August 28, 2020
Copyright © Keniti Sato. All Rights Reserved.