An almost sure invariance principle for partial sums associated with a random field

Carla C. Neaderhouser

Stochastic Processes and their Applications, 1981, vol. 11, issue 1, 1-10

Abstract: Conditions under which the partial sums of an array of weakly dependent random variables (Xn)n[epsilon]Zd,d [greater-or-equal, slanted]1, are almost surely asymptotically close to standard Brownian motion are derived. For such arrays, which include certain Gibbs random fields from statistical mechanics, the asymptotic behavior of the partial sums is thus a consequence of known results about Brownian motion.

Date: 1981
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