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Asymptotics for randomly weighted and stopped dependent sums
Stochastics, 2015This paper deals with the tail probability of , where is a sequence of extended negatively upper orthant dependent or bivariate upper tail independent, identically distributed random variables with dominatedly varying tails, is a sequence of nonnegative nondegenerate at zero random variables (not necessarily independent and identically distributed), is
Yang Yang +2 more
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Moments of randomly stopped sums-revisited
Journal of Theoretical Probability, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Tail areas for randomly stopped sums defined on a Markov chain
Communications in Statistics. Stochastic Models, 1993Summary: A saddlepoint approximation is provided for the tail area \(P\left\{\sum^ N_ 1X_ k>y\right\}\) where the \(S_ n=\sum^ n_ 1X_ k\) form a random walk on a Markov chain and \(N\), which is independent of the \(X_ k\), has a negative binomial distribution.
Homble, P., McCormick, William P.
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Randomly stopped sums of not identically distributed heavy tailed random variables
Statistics & Probability Letters, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Danilenko, Svetlana, Šiaulys, Jonas
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Finiteness of moments of randomly stopped sums of i.i.d. random variables
Statistics & Probability Letters, 1989Let \(\{X_ n\), \(n\geq 1\}\) be independent, identically distributed random variables such that \(E(X)=0\), and let \(Z_ n=\sum^{n}_{i=1}X_ i\). If N is a stopping time for \(\{X_ n\}\), \(Z_ N\) is called a randomly stopped sum. The main result of this paper states that for \(r\in (0,\infty)\) and \(a\in [1,2]\), \(E(N^{r/a})
Ghahramani, Saeed, Wolff, Ronald W.
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A note on second moment of a randomly stopped sum of independent variables
Statistics & Probability Letters, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
de la Peña, Victor H. +1 more
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On the existence of the expectation of randomly stopped sums
Journal of Applied Probability, 1967Let a+ = a if a > 0, a+ = 0 otherwise, and a– = (– a)+.
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A Law of the Iterated Logarithm for Randomly Stopped Sums of Heavy Tailed Random Vectors
Monatshefte f�r Mathematik, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Scheffler, Hans-Peter +1 more
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On a conjecture for the non-existence of the expectation of randomly stopped sums
Journal of Applied Probability, 1995In a recent paper on the validity of Wald's equation, Roters (1994) raised an important question on the non-existence of the expectation of randomly stopped sums. The purpose of this note is to answer the question in the affirmative. As a consequence, an old question by Taylor (1972) also gets a positive answer.
Lefèvre, Claude, Utev, Sergej
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