- Research Group Linkage Singular diffusions: analytic and stochastic approaches  (2018-2022)

funded by the Alexander von Humboldt Foundation between the Institute of Mathematics of the University of Potsdam and the Institute of Mathematics at the National Academy of Sciences of Ukraine,. This alumni programme allows sponsorship by the Alexander von Humboldt Foundation of long-term research collaborations between academics in Germany and abroad.

Brief summary of the scientific project:

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.

This Research Group Linkage provides funding mainly for reciprocal research visits and for scientific Conferences.

The first Conference took place inPotsdam (Am Neuen Palais, see the picture) April 1 - 3, 2019:

Workshop "Singular diffusions: analytic and stochastic approaches I"

See also the press article p. 33 in Portal 1/2019.

The second Conference  was planed for 2020 but should be delayed due to the pandemic of Covid-19. It was then planed for the Spring 2022 but then cancelled because of the war in Ukraine.

- DAAD Leonhard-Euler Program (2012-2014).

Cooperation with University T. Shevchenko in Kyiv.

2012-2013: Project ID 55518603 Analyse feiner Eigenschaften zufälliger Prozesse.

2013-2014: Project  ID 57044593 Feine Eigenschaften stochastischer Prozesse.

In that framework organisation of two minicourses done in Berlin/Potsdam from Prof. Alexei Kulik (March 2013) entitled "Ergodic rates for Markov chains and processes" and from Prof. Andrey Pilipenko (December 2013) entitled "Stochastic differentional equations with reflection", published by Potsdam University Press.

The following Ukrainian students obtained founds to visit Potsdam University: Daryna Soboleva, Tetiana Kosenkova, Taras Tymoshkevych, Vitalii Senin and Yurii Ganychenko.

- Agreement on research, educational and cultural cooperation (2013-2016) between the Faculty of Science of the University of Potsdam (Germany) and the Mechanics and Mathematics Faculty of Taras Shevchenko National University of Kyiv (Ukraine)

- DAAD Research Grant for young academics  (2016-2017)

for the postdoctoral researcher Dr. Yurii Ganychenko.

- Alexander von Humboldt Georg Forster-Fellowship  (2017-2019)

for the postdoctoral researcher Dr. Yurii Ganychenko.

- MASH European-Fellowship  (2019)

for the undergraduate student Oleksandr Prykhodko. See here his Preprint.