Shinzo Watanabe

Shinzō Watanabe (渡辺 信三 Watanabe Shinzō, 23 December 1935) is a Japanese mathematician, who has made fundamental contributions to probability theory, stochastic processes and stochastic differential equations.[1]

Shinzō Watanabe
渡辺 信三
Born(1935-12-23)December 23, 1935
NationalityJapanese
Alma materUniversity of Kyoto
Known for
AwardsAutumn Prize of the Japan Mathematical Society (1989)
Japan Academy Prize (1996)
Scientific career
FieldsStochastic analysis
InstitutionsUniversity of Kyoto
Doctoral advisorKiyosi Itô
Doctoral studentsTakashi Kumagai
Shinnichi Kotani
InfluencesKiyosi Itô, Paul Lévy, Paul Malliavin

Biography

Watanabe received his bachelor's degree from Kyoto University in 1958 and completed his Ph.D. under Kiyosi Itô in 1963.[2] Watanabe subsequently became a professor at Kyoto University. He was also a visiting professor at Stanford University and participated in the organizing committees of international Japanese/Soviet seminars on probability theory.

Scientific contributions

Watanabe has made many important contributions to stochastic analysis and the theory of stochastic processes. In an important work with H. Kunita, he extended K. Ito's theory of stochastic integration, initially developed by Ito for Markov processes, to square integrable martingales. [3] This theory, known as the 'Kunita-Watanabe extension' is based on the crucial 'Kunita-Watanabe inequality' for the stochastic integral.[4]

Another important contribution of Watanabe has been to use the Malliavin calculus to establish a theory of generalized functionals on Wiener space, by analogy to Laurent Schwartz's theory of distributions, and apply this theory to obtain expansions of heat kernels. [5]

Watanabe also made important contributions to the study of multidimensional diffusion processes with boundary conditions [6] and continuous-time branching processes.[7]

Awards and honours

In 1989 he received the Autumn Prize of the Mathematical Society of Japan.[8]

In 1983 he was an invited speaker at the International Congress of Mathematicians in Warsaw (Excursion point processes and diffusion). In 1996 he received the Japan Academy Prize in Mathematics.[9]

Selected publications
  • Noboyuki Ikeda, Shinzo Watanabe: Stochastic differential equations and diffusion processes. North Holland. 1981. 2nd edition. 1989. MR 1011252.
  • with Toshio Yamada: Yamada, Toshio; Watanabe, Shinzo (1971). "On the uniqueness of solutions of stochastic differential equations". J. Math. Kyoto University. 11: 155–167. doi:10.1215/kjm/1250523691. MR 0278420.
  • Watanabe, Shinzo (1969). "On two dimensional Markov processes with branching property". Trans. Amer. Math. Soc. 136: 447–461. doi:10.1090/s0002-9947-1969-0234531-1. MR 0234531.
  • Watanabe, Shinzo (1968). "A limit theorem of branching processes and continuous state branching processes". J. Math. Kyoto University. 8: 141–167. doi:10.1215/kjm/1250524180. MR 0237008.
  • Limit theorem for a class of branching processes, in: Markov processes potential theory, Proc. Symp. Univ. Wisconsin, Madison, 1967, 205-232

References
  1. Dynkin collection
  2. Shinzo Watanabe at the Mathematics Genealogy Project
  3. Kunita, Hiroshi; Watanabe, Shinzo (1967). "On square integrable martingales". Nagoya Math. J. 30: 209–245. doi:10.1017/S0027763000012484.
  4. http://www-math.mit.edu/~dws/ito/ito7.pdf
  5. Watanabe, Shinzo (1987). "Analysis of Wiener Functionals (Malliavin Calculus) and its Applications to Heat Kernels". Annals of Probability. 30: 1–39. doi:10.1214/aop/1176992255.
  6. Watanabe, Shinzo (1971). "On stochastic differential equations for multi-dimensional diffusion processes with boundary conditions". J. Math. Kyoto University. 11: 169–180. doi:10.1215/kjm/1250523692.
  7. Watanabe, Shinzo (1968). "A limit theorem of branching processes and continuous state branching processes". J. Math. Kyoto University. 8: 141–167. doi:10.1215/kjm/1250524180. MR 0237008.
  8. MSJ Iyanaga Spring and Autumn Prize
  9. https://projecteuclid.org/download/pdf_1/euclid.pja/1195510318


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