For a sequence {X-n, n >= 1} of random variables, set Y-n = max(1 <= k <= n)X(k) - a(n), where {a(n), n >= 1} is a sequence of constants to be specified. We obtain the limiting behavior of the sequences of positive and negative parts of {Y-n, n >= 1} when the tail distribution of {X-n, n >= 1} satisfies suitable "exponential-type" conditions. Next, we consider the rate convergence of the positive part to zero (results similar to complete convergence).

On the asymptotic behavior of the sequence and series of running maxima from a real random sequence

GIULIANO, RITA;
2013

Abstract

For a sequence {X-n, n >= 1} of random variables, set Y-n = max(1 <= k <= n)X(k) - a(n), where {a(n), n >= 1} is a sequence of constants to be specified. We obtain the limiting behavior of the sequences of positive and negative parts of {Y-n, n >= 1} when the tail distribution of {X-n, n >= 1} satisfies suitable "exponential-type" conditions. Next, we consider the rate convergence of the positive part to zero (results similar to complete convergence).
Giuliano, Rita; Ngamkham, T.; Volodin, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/212136
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