Limiting behavior of the stochastic processes, stochastic analysis, martingale and other stochastic inequalities, limit theorems for U-statisctics and theory of random chaos, applications to geometry of convex sets and theory of graphs.
Theory of random chaoses and U-statistics; estimations of tails and moments, limit theorems. Probabilistic methods in analysis and convex geometry, stochastic inequalities
Diffusion processes on fractals, differential inequalities and their applications in probability, Levy processses and nonlocal operators, Levy processes in random enviroment
Stochastic analysis, stochastic processes in the space of distributions, limit theorems for empirical processes related to particle systems; analysis of the corresponding limit processes