科研之友
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摘要
Given a field of independent identically distributed (i.i.d.) random variables {X((n) over bar); (n) over bar is an element of N(d)} indexed by d-tuples of positive integers and taking values in a separable Banach space B, let X((n) over bar)((r)) = X((m) over bar) if parallel to X((m) over bar)parallel to is the r-th maximum of {parallel to X((k) over bar)parallel to; (k) over bar <= (n) over bar} and let ((r))S((n) over bar) = S((n) over bar) - (X((n) over bar)((1)) + ... + X((n) over bar)((r))) be the trimmed sums, where S((n) over bar) = Sigma((k) over bar <=(n) over bar) X((k) over bar). This paper aims to obtain a general law of the iterated logarithm (LIL) for the trimmed sums which improves previous works.
