Strong law of large numbers for unions of random closed sets

Ilya S. Molchanov

Stochastic Processes and their Applications, 1993, vol. 46, issue 2, 199-212

Abstract: The almost sure limit for the random closed set Xn=a-1n(A1 [union or logical sum]...[union or logical sum] An) is found where an tends to infinity and A1,...,An are i.i.d. copies of a certain random closed set A. The established strong law of large numbers for unions of random sets generalizes previous results on almost sure limits for samples of random vectors.

Keywords: random; set; *; almost; sure; limit; *; convergence; of; sets; *; capacity; *; regular; variation (search for similar items in EconPapers)
Date: 1993
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