Stochastic Convergence of Sequences of Random Vectors Cover Image

Zbieżność stochastyczna ciągów wektorów losowych
Stochastic Convergence of Sequences of Random Vectors

Author(s): Jan Tatar
Subject(s): Economy, Methodology and research technology
Published by: Wydawnictwo Uniwersytetu Ekonomicznego w Krakowie
Keywords: power of vector; moment of probability distribution; random vector; stochastic convergence;

Summary/Abstract: The paper presents a multidimensional generalisation (known for one-dimensional random variables) of two theorems regarding stochastic convergence – that is, convergence by probability. The generalised theorems are Markov’s and Chinchyn’s weak laws of great numbers. Both lead to the theory that, with the appropriate assumptions, a sequence of arithmetic averages of the random vectors converges their expected values to the arithmetic average. The proof for this thesis uses „whole moments of the multidimensional probability distribution”, which the author has proposed elsewhere. Their basis is a definition of the power of a vector in a space with a scalar product.

  • Issue Year: 965/2017
  • Issue No: 5
  • Page Range: 107-116
  • Page Count: 10
  • Language: Polish