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Strongly consistent estimates are shown, via relative frequency, for theprobability of "white balls" inside a dichotomous urn when such a probabilityis an arbitrary continuous time dependent function over a bounded timeinterval. The asymptotic behaviour of relative frequency is studied in anonstationary context using a Riemann-Dini type theorem for SLLN of randomvariables with arbitrarily different expectations; furthermore the theoreticalresults concerning the SLLN can be applied for estimating the mean function ofunknown form of a general nonstationary process.

Asymptotics for relative frequency when population is driven by arbitrary evolution