Strong Law of Large Numbers for Multilinear Forms

Anda Gadidov

Gannon University

Let tex2html_wrap_inline21 be a non-negative integer and let tex2html_wrap_inline23 , tex2html_wrap_inline25, be m independent sequences of independent and identically distributed symmetric random variables. Define tex2html_wrap_inline29 , and let tex2html_wrap_inline31 be a non-decreasing sequence of positive numbers, tending to infinity and satisfying some regularity conditions. For m=2 necessary and sufficient conditions are obtained for the strong law of large numbers tex2html_wrap_inline35 to hold, and for m>2 the strong law of large numbers is obtained under a condition on the growth of the truncated variance of the tex2html_wrap_inline39 .

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Wed Aug 13 13:54:29 EDT 1997