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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Probability and Stochastic Analysis


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.



  • Concentration of measure, probability in Banach spaces, U-statistics, random matrices, probabilistic methods in convex geometry
  • Levy processes, subordinate Brownian motion
  • General theory of processes and their connections with functional analysis and approximation theory; majorizing measures techniques
  • Martingale inequalities, Bellman function method
  • Stochastic processes
  • Stochastic analysis; applications to financial mathematics
  • Theory of random chaoses and U-statistics; estimations of tails and moments, limit theorems. Probabilistic methods in analysis and convex geometry, stochastic inequalities
  • Markov chains, concentration inequalities.
  • Lower and upper bounds for stochastic processes
  • Tail and moments bounds for random multilinear forms
  • Stochastic analysis, branching particle systems, limit theorems for branching systems, superprocesses
  • Comutative and noncomutative martingale inequalities, Burkholder method
  • Stochastic inequalities, probabilistic methods in analysis, graph theory, discrete harmonic analysis and convex geometry
  • Diffusion processes on fractals, differential inequalities and their applications in probability, Levy processses and nonlocal operators, Levy processes in random enviroment
  • Inequalities for maximal operators, Bellman function method
  • Bounds for sums of random vectors, probabilistic methods in convex geometry
  • Concentration of measure; martingale inequalities with applications to analysis
  • Stochastic analysis, stochastic processes in the space of distributions, limit theorems for empirical processes related to particle systems; analysis of the corresponding limit processes
  • Self-similar processes and limit theorems for particle systems