Shinzō Watanabe (渡辺信三 Watanabe Shinzō, 23 December 1935) is a Japanese

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, who has made fundamental contributions to

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

stochastic processes In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appe ...

and stochastic differential equations.Dynkin collection
/ref> He is regarded and revered as one of the fundamental contributors to the modern probability theory and Stochastic calculus. The pioneering book “Stochastic Differential Equations and Diffusion Processes” he wrote with Nobuyuki Ikeda has attracted a lot of researchers into the area and is known as the “Ikeda-Watanabe” for researchers in the field of stochastic analysis. He had been served as the editor of Springer Mathematics.

Biography

Watanabe received his bachelor's degree from

Kyoto University , mottoeng = Freedom of academic culture , established = , type = National university, Public (National) , endowment = ¥ 316 billion (2.4 1000000000 (number), billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff ...

in 1958 and completed his Ph.D. under

Kiyosi Itô was a Japanese mathematician who made fundamental contributions to probability theory, in particular, the theory of stochastic processes. He invented the concept of stochastic integral and stochastic differential equation, and is known as the fo ...

in 1963. Watanabe subsequently became a professor at Kyoto University. He was also a visiting professor at

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

and participated in the organizing committees of international Japanese/Soviet seminars on probability theory. He has one daughter Shiori Watanabe.

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. This theory, known as the ''Kunita-Watanabe extension'' is based on the crucial ''

Kunita–Watanabe inequality In stochastic calculus, the Kunita–Watanabe inequality is a generalization of the Cauchy–Schwarz inequality to integrals of stochastic processes. It was first obtained by Hiroshi Kunita and Shinzo Watanabe and plays a fundamental role in thei ...

'' for the stochastic integral. Another important contribution of Watanabe has been to use the Malliavin calculus to establish a theory of generalized functionals on

Wiener space In mathematics, classical Wiener space is the collection of all Continuous_function#Continuous_functions_between_metric_spaces, continuous functions on a given domain of a function, domain (usually a subinterval of the real line), taking values i ...

, by analogy to

Laurent Schwartz Laurent-Moïse Schwartz (; 5 March 1915 – 4 July 2002) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 19 ...

's theory of distributions, and apply this theory to obtain expansions of heat kernels. Watanabe also made important contributions to the study of multidimensional diffusion processes with boundary conditions and continuous-time branching processes.

Awards and honours

In 1989 he received the Autumn Prize of the Mathematical Society of Japan. In 1983 he was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...

(''Excursion point processes and diffusion''). In 1996 he received the Japan Academy Prize in Mathematics.https://projecteuclid.org/download/pdf_1/euclid.pja/1195510318

Selected publications

* Noboyuki Ikeda, Shinzo Watanabe: * with Toshio Yamada: * * * Limit theorem for a class of branching processes, in: Markov processes potential theory, Proc. Symp. Univ. Wisconsin, Madison, 1967, 205-232

References

External links

On discontinuous additive functionals and Levy measures of a Markov process / By Shinto WATANABE (Received July 15, 1964)

The Japanese Contributions to Martingales Shinzo WATANABE / Journ@l électronique d’Histoire des Probabilités et de la Statistique/ Electronic Journal for History of Probability and Statistics . Vol.5, n°1. Juin/June 2009
1935 births Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians Probability theorists Kyoto University alumni Kyoto University faculty {{Japan-bio-stub