Martingale convergence, series expansion of Gaussian elements, and strong law of large numbers in Fréchet spaces

Gian-Carlo Mangano

Journal of Multivariate Analysis, 1976, vol. 6, issue 2, 319-329

Abstract: The main result of this paper is the derivation of a convergence theorem for certain martingales with values in a separable Fréchet space F. It is shown that this result includes a well known theorem due to Chatterji. Moreover, the series expansion of zero-mean Gaussian elements with values in F and the strong law of large numbers for i.i.d. F-valued random elements also follow as applications of the main theorem.

Keywords: Random; elements; in; a; topological; vector; space; martingales; in; a; topological; vector; space; Bochner-intergrability; Gaussian; random; elements; reproducing; kernel; Hilbert; space; series; expansion; of; zero-mean; Gaussian; elements; strong; law; of; large; numbers (search for similar items in EconPapers)
Date: 1976
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