SINGULAR DIFFUSIONS: AN ANALYTIC AND STOCHASTIC APPROACHES

Official partner of the project:

• Institute of Mathematics, National Academy of Sciences of Ukraine;

• Kyiv Academic University, Ukraine;

• Institute of Mathematics of Potsdam University, Germany.

Funding:

Alexander von Humboldt Foundation

Duration:

2018-2021

Coordinators:

• Antoniouk A.V. (Institute of Mathematics, National Academy of Sciences of Ukraine);

• Pilipenko A. Yu. (Institute of Mathematics, National Academy of Sciences of Ukraine);

• Roelly S.( Institute of Mathematics of Potsdam University, Germany).

Summary:

Modern investigations in applied sciences, such as ecology, chemistry, hydrology, queuing theory, etc., demands mathematical models of dynamics involving non regular parameters.

Nowadays, operator theory or stochastic dynamics with smooth coefficients evolving in domains with regular boundary is well-understood. However the irregular cases remain a big challenge to solve, either via analytical methods or via probabilistic methods. The close connection between the stochastic approach and the analytic one is well known since long time. For example, transition densities of solutions to stochastic differential equations (SDEs), exit moments or various functionals of solutions to SDEs are related with fundamental solutions, Green functions of the corresponding partial differential equations. Nevertheless in spite of rather elaborated technology from both mathematical domains in singular case there is a lack of adequate approaches.

This challenge is the main issue of this project. We plan joint efforts directed to the common problems and will stimulate the bilateral cooperation between the scientists in both disciplines belonging to the partner institutions. Especial stress will be done to the involvement of the young scientists from both sides in this cooperation.