Synthetic Research of Probability Theory

点击翻译按钮获取中文摘要

This research was accomplished by 25 members under strong helps from many researchers in probability theory and related fields. During three years of the research period, 27 meetings were organized and 21 researchers were invited from abroad. A lot of research products were obtained in broad area:1. Related to the basic theory in probability theory, extension of the inverse arcsine law to one dimensional diffusion processes, properties of Brownian motion/heat kernel/Green function on several spaces, Markov processes and Dirichlet form, infinite dimensional stochastic analysis, stationary phase method and asymptotic theory and others were discussed.2. As applications of probability theory, mathematical physics such as analysis of phase separating surface arising under phase transitions, derivation of free boundary problem, motion of interacting Brownian hard balls, scaling limit of percolation cluster, random matrix, stochastic processes on fractals, problem of risk sensitive stochastic control, ergodid theory especially law of large numbers for ψ-mixing random variables, numerical calculation for stochastic differential equations and nonlinear diffusion equations, asymptotic expansion and applications of Malliavin calculus in mathematical statistics, problems related to differential geometry like collapse of manifolds.Concrete explanations on each research result can be found in the booklet of the research report in details. As is stated above, under the project of this research, many foreign researchers were invited and it was very fruitful and extremely important for the development of the probability theory in Japan in future.