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Stochastic Convergence of Sequences of Random Vectors

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.

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