Essentials of Stochastics

  1. Classical definition of probability, and classical probability problems of calculation of chances. Elements of combinatorics.
  1. Classical statistical problems and methods (astronomy, geodesy; least-squares method, maximum-likelihood method.
  1. Law of large numbers of J.Bernoulli («Ars conjectandi», 1713). The de Moivre--Laplace and Poisson theorems.
  1. Axiomatics of Kolmogorov. Concepts of probability space.
  1. Basic notions of probability theory (random variable, expectation, characteristic function,...).
  1. Stochastic (random) processes: construction and models.
  1. Basic classes of stochastic processes (Markov processes, stationary processes,...).
  1. Diffusion processes (by Kolmogorov and Ito).
  1. Martingales and related processes.
  1. Basic problems and methods of mathematical statistics.