On Chung's type law of large numbers for fuzzy random variables

초록

Let {X-n vertical bar n >= 1} be a sequence of independent fuzzy random variables and {a(n)vertical bar n >= 1} a sequence of positive real numbers converging to infinity. In this paper we show that, under the assumption Sigma(infinity)(n = 1) E phi(parallel to X-n parallel to(rho p))/ phi(a(n)) < infinity-with some restrictions on phi, S-n/a(n) -> 0 a.s. if and only if S-n/a(n) -> 0 in probability if and only" if S-n/a(n) -> 0 in L-1 where S-n = Sigma(n)(i-l) X-i. This will generalize earlier results of strong law of large numbers for random elements in a Banach space (Choi and Sung (1988). Bull. Austral. Math. Soc. 37, 93-100). (c) 2005 Elsevier B.V. All rights reserved.

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