Determining the form of the mean of a stochastic process

Carl Spruill

Journal of Multivariate Analysis, 1977, vol. 7, issue 2, 278-285

Abstract: Let [mu] be the mean function of an observable stochastic process whose sample paths fall in some Banach space with a basis and assume [mu] is also in this space. A procedure like Cover's (Ann. Statist.1, 862-871, 1973) is given which has the property that if the last nonzero coordinate of [mu] is the mth then with probability one this is discovered after at most a finite number of erros. If [mu] has an infinite number of nonzero coordinates, then with probability one this is discovered after at most a finite number of errors except for a set of [mu] of prior probability zero.

Keywords: mean; of; a; process; Banach; space-valued; random; variables; law; of; the; iterated; logarithm; nonterminating; decision; procedures; estimation; of; [sigma]2; Gaussian; processes (search for similar items in EconPapers)
Date: 1977
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