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The Probability summer school, organized by the MCA, has been successfully finished

The school on probability theory was held from 17 to 29 August. Students and young researchers from different cities of Russia, Ukraine and Uzbekistan attended a course on stochastic differential equations read by professor Alexander Yuryevich Veretennikov of the Higher School of Economics and professor Daria Lukyanova of the University of Evry (France), and an introductory course on the theory of large deviations by Artyom Vasilyevich Logachev, a research fellow of the Mathematical Center in Akademgorodok. As a follow-up to the lectures and seminars, the students went over the material they had learned. Seminars on stochastic differential equations were conducted by a young scientist Maria Aleksandrovna Veretennikova from the University of Warwick (Great Britain). 

The first part of the school was devoted to stochastic differential equations and coverd the following topics:

  • Wiener process and its properties. Stochastic Ito integral, its properties. Martingales, sub and supermartingales; simplest (sub) martingale inequalities.
  • Ito's formula. Stochastic exponents and Girsanov's theorem.
  • Stochastic differential equations (SDE). Weak and strong decisions.
  • Connection of SDEs with partial differential equations. Markov Property of Solutions to SDEs.
  • SDEs with jumps.

During the second part of the school, the students got started with the theory of large deviations and its applications to stochastic differential equations, namely:

  • Large deviation theory for sums of independent random variables.
  • Large and moderately large deviation principle for sums of independent random variables.
  • Large deviation theory for trajectories of a Wiener process.
  • Contractional principle. Large deviation principle for solutions of stochastic equations with constant diffusion coefficient.

The school was supported by the Mathematical center in Akademgorodok.

One of the participants of the school, a 4th year undergraduate student of department of Mechanics and Mathematics of the NSU Timur Ruslanovich Kusnatdinov , shared his impressions:

In addition to the traditional lessons in the form of lectures and seminars, course participants gathered to discuss the concepts introduced and the theorems proved. The purpose of these meetings was to gain a deeper understanding of the material. Perhaps, it was this part of the program that was most interesting, thanks to inquisitive and active colleagues, to whom I’m giving special thanks.

And here is a comment from another 4th year undergraduate student of department of Mechanics and Mathematics of the NSU Roman Sergeevich Ishkov:

I would like to thank all the organizers of the Probability school—especially Tesemnikov Pavel Igorevich—for their efforts in delivering the lectures, managing the follow-up on these lectures andrecording these lectures on video. I would like to specially thank the lecturers for their time and effort on teaching these courses to us. I can say that the material was rather difficult, but presented in an accessible and interesting form.

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