Laws of Large Numbers for $D\lbrack0, 1\rbrack$

Laws of large numbers for

“…The case of nonidentical distributions for Proposition A was studied by Daffer and Taylor (1979) using a method based on the properties of the Skorohod metric. In this paper we are interested in investigating the case of nonidentical distributions by combining the classical result of Kuelbs and Zinn (1979) on the law of large numbers in the measurable spaces and the techniques we introduced in Bezandry and Fernique (1992) and Fernique (1994) to study the convergence in distribution in D. Let us first recall the result of Kuelbs and Zinn (1979).…”

Mathematical Statistics and Limit Theorems

“…Concerning the strong law of large numbers for independent D-valued random variables it appears in Daffer and Taylor (1979): they study the case where X is convex tight and the case where X belongs to the cone of non-decreasing elements of D. For linear processes in D observed in continuous time, see El Hajj (2011). See also Schiopu-Kratina and Daffer (1999), Bezandry (2006) and Ranga Rao (1963).…”

Some Strong and Weak Laws of Large Numbers in D(0,1).

“…as convex tightness and conditions on the moments E IXn Ir and others ( [4], [13], [14],112]). For random elements in a Banach space E, convexity conditions on E can be assumed, but such con- [13],[141, [12]), some of which are listed in §3 and investigated in 16.…”