Displaying similar documents to “Subgaussian random variables in Hilbert spaces”

Strong laws of large numbers in certain linear spaces

Wojbor A. Woyczynski (1974)

Annales de l'institut Fourier

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In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous F -norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors. ...

A vectorial expression for Liapounov's central limit theorem.

Ramón Ardanuy, Angel Luis Sánchez (1992)

Extracta Mathematicae

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In this paper we prove two Liapounov's central limit theorems for a sequence of independent p-dimensional random vectors, with mean and variance and covariance matrix ∑n, in cases of both general and uniformly bounded sequence.