Since the founding of the mathematical theory of stochastic differential equations by Kiyosi Itô in 1942, research on stochastic calculus in Japan has had a great influence on the development of probability theory throughout the world. Probability theory itself has grown remarkably over the last century, and now encompasses an extremely wide range of research topics. Within mathematics, it has strong interactions with fields such as partial differential equations, potential theory and geometry. Moreover, the vast expansion of probability research is directly linked to applications across the sciences, in areas such as statistical mechanics, biology, economics and the analysis of big data. As a result of probability theory now having so many different aspects, it is difficult for individual researchers to grasp the subject in its entirety.

With the keywords "stochastic processes and stochastic analysis", this RIMS Research Project aims to further promote international joint research in probability by disseminating results in the area that originate in Japan. Centering on the following three themes, the program will provide a bird's-eye view of modern probability theory. (For each theme, a conference is planned, the title of which is shown in parentheses.)
(i) Stochastic Processes Related to Stochastic Partial Differential Equations (Stochastic Partial Differential Equations and Stochastic Calculus)
(ii) Analysis of Stochastic Models Motivated by Statistical Mechanics (Stochastic Analysis on Large Scale Interacting Systems)
(iii) Random Matrix Theory, Combinatorial Probability and Quantum Information (Random Matrices and Their Applications)
Furthermore, to inspire exchanges between these themes, in September 2023, we will organize a large-scale conference at the Research Institute for Mathematical Sciences, inviting researchers in stochastic processes and stochastic analysis who are active at the front line of probability research internationally.

Mid-career researchers will take responsibility for the practical organization of conferences on each theme and, in doing so, will promote the participation of young researchers, including as speakers, so that the next generation of researchers plays an active role. We encourage the participation of female researchers in all aspects of the program, seeing it as an opportunity to promote gender diversity in research on probability theory in Japan.