AWARDEE OF MATHEMATICS AND MECHANICS PRIZE

WANG ZIKUN

Wang Zikun, born in Ji An, Jiang Xi Province of China; mathematician and educator, majoring in probability theory and mathematical statistics; professor of Nankai University (1956-1984); Professor of Beijing Normal University (1984-present); president of Beijing Normal University (1984.5-1989.5); director of the Research Institute of Mathematics of Shantou University (1993-1999).
Education experience:
Graduated from Department of Mathematics of Wuhan University in 1952.
Graduated from Department of Mathematics and Mechanics of Moscow University with Ph. D. (Candidate) in 1958.
Acquired Honoring Degree of Doctor of Science from Macquarie University of Australia in 1988.
Elected the academician of the Chinese Academy of Sciences in 1991.
Main research work:
(1) In 1960's, Wang gave the construction of all birth and death processes with a general given transition density, solving completely the construction problem for birth and death processes. The worldwide famous probabilist W. Feller was also studying this problem at that time, using analytic methods. Wang used the probabilistic methods of passage to the limit invented by himself. The advantage of Wang's method lies in its efficiency and clearness, which gave all birth-death processes and showed the clear probabilistic intuition. Based on this construction, Wang obtained the distributions of some integral functionals of birth and death processes. The research results of Wang were cited and evaluated highly by some famous probabilists including E.B. Dynkin, A.A. Yushekevich, D.G. Kendall and so on.
(2) About general Markov processes, Wang proved that for a process to have the strong tail 0-1 law if and only if all its bounded harmonic functions are constants; and for the process to be recurrent if and only if all its excessive functions are constants.
(3) Wang initiated the study of stochastic functional analysis in China and proved some limit theorems of random elements in the space of distributions. This research inspired related investigation of a number of probabilists from Sichuan University, Xiamen University, Qingdao Ocean University and so on.
(4) In 1970's, Wang concentrated his study on the relationship between Markov processes and potential theory. He obtained the joint distribution of the last exit time and the last exit point from a sphere as well as the distribution of the maximum excursion for Brownian motion and symmetric stable process. At about the same time, R.K. Getoor from U.S.A. obtained independently the distribution of last exit time for Brownian motion.
(5) Wang was also the earliest probabilist in China to study multiparameter Ornstein-Uhlenbeck processes. In 1983, he gave a definition of the process by a stochastic integral relative to a time-space white noise. One year later, J. B. Walsh gave an equivalent definition in 1984. Wang studied multiparameter and infinite dimensional Ornstein-Uhlenbeck processes in 1999, and obtained a sufficient and necessary condition for the absolute continuity of two different distributions with respect to each other.
(6) Since 1990, Wang and his group have been studying superprocesses, a class of measure-valued Markov processes. Wang obtained some results on this topic including a power series expansion of those processes. His colleagues and students have obtained further results.
(7) As the applications of probability theory, Wang created simulations on computers of some stochastic processes used for navigations. Jointly with scientists from the National Earthquake Bureau, Wang established a number of statistical methods used in forecasting earthquakes.
In addition, during his term as the president of Beijing Normal University in 1984, Wang called on the society for “honoring teachers and respecting education"; he suggested setting up “A Teacher's Day" with some other famous scholars, and such a day has been established (1985) in China. In 1977, he published his well-known book entitled “Talks on Scientific Discovery" (in Chinese). This was the first book on the popularization of science published in China after Its “Opening up" and has made very good influence on the youth.