A martingale is a random sequence (or process) that remains constant on average in the future. Martingales are widely used in probability theory and, in particular, in stochastic calculus, as well as in various applications, for example, in financial mathematics. The purpose of this course is to introduce students to the basic concepts and results of martingale theory. Some applications of martingales in financial mathematics will also be discussed. The whole presentation will be carried out for the case of discrete time. For understanding of the course, only the knowledge of the standard course of probability theory is required.

Просьба к участникам обращаться к Михаилу Валентиновичу Житлухину, mikhailzh@mi-ras.ru, за данными для подключения к занятиям через Zoom.

Financial support. The course is supported by the Simons Foundation and the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Lecturer
Zhitlukhin Mikhail Valentinovich

Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center