A martingale is a random sequence (or process) which stays constant on average in the future. Martingales are widely used in probability theory, especially in stochastic calculus and its various applications, for example, in mathematical finance. The goal of this course is to present basic notions and results of the theory of martingales: definitions and main properties, convergence theorems, martingale inequalities, connections with sequences of densities of probability measures. All results will be presented for the case of discrete time. The only prerequisite is a standard course in probability theory.

Financial support. The course is supported by 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).

Program

Lecturer
Zhitlukhin Mikhail Valentinovich

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