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

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  • Mangano, Gian-Carlo

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.

Suggested Citation

  • Mangano, Gian-Carlo, 1976. "Martingale convergence, series expansion of Gaussian elements, and strong law of large numbers in Fréchet spaces," Journal of Multivariate Analysis, Elsevier, vol. 6(2), pages 319-329, June.
    • Handle: RePEc:eee:jmvana:v:6:y:1976:i:2:p:319-329
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