The French-German graduate school Potsdam-Toulouse called ** Stochastic processes and statistical machine learning**is funded by the French-German University for the period 2018-2021. It involves mathematicians of both universities. Aims of this binational doctoral structure named

- Integration of doctoral students into a common larger research programm

- Scientific education by specialized serial lectures, short term and long term visits of guest scientists, workshops

- Increase of the mobility of young researchers (a typically 6-12 month's stay at the foreign partner university)

- Possibility of novel international collaborations

- Possibility of joint PhD-supervisions by two scientific teams from distinct countries.

The concerned mathematics research domains are the **Probability Theory** - in particular the field of stochastic processes- and the mathematical statistics - inparticular the field of **Statistical Learning**.

French speaker: Prof. **Patrick Cattiaux**

German speaker: Prof. **Sylvie Roelly**

**Workshop "Stochastic processes and statistical machine learning I"**

Potsdam, 14-16 February 2018

**Workshop "Stochastic processes and statistical machine learning II"**

Toulouse, 13-15 March 2019

**Workshop "Stochastic processes and statistical machine learning III"**

Potsdam, March 25- 26th 2021

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 in Potsdam (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 one was planed for 2020 but should be delayed due to the pandemic of Covid-19.

- **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.

Since several years the Chair of Probability develops scientific collaborations with Dr. M. Högele, from *Universidad de los Andes*. See e.g. the publications.

Since 2016, the University Potsdam funded - in the framework of the Programme KoUP - a yearly Workshop in Bogotá organised jointly by the Chair of Probability (Potsdam) and the department of Mathematics of the *Universidad de los Andes*.

2016:**Random models with applications in the natural sciences**

2017:**Stochastic processes with applications in the natural sciences**

2018: **Random and spectral methods with applications in statistical physics**

The proceedings of the 2016 Winterschool/Workshop are published by the Potsdam University Press. One finds here the digital version.

In Spring term 2018, the researcher Samuel Sindayigaya from Ruhengeri (Rwanda) visited the Chair of Probability. His joint research project concerning birth-death random models with incidence of a partial catastrophe ended with the research paper *Random population dynamics under catastrophic events* published in 2022 in Journal of Applied Probability, 59-4 with co-authors P. Cattiaux, J. Fischer and S. Roelly.

The French-German graduate school Potsdam-Nanterre called *Applications of S*

This binational doctoral structure named **CDFA 01-06 **allowed to integrate youg researchers into a common larger research programm, to organize specialized serial lectures abroad, short term visits of guest scientists, and a yearly workshop.

Moreover a joint PhD-supervision of R. Murr took place.

French speaker: Prof. **Christian Léonard**

German speaker: Prof. **Sylvie Roelly**