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Conditions for Finite Ladder Height and Delay Moments
Operations Research, 1984We provide simple proofs for several known results: conditions for finite ladder height moments are obtained in a unified way for random walks under both the oscillating and drift cases. The random walk conditions are used to obtain conditions for finite delay moments for the GI/G/1 queue.
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Exact expressions for the moments of ladder heights
Siberian Mathematical Journal, 2010Let \(X_1, X_2,\dots, X_n,\dots\) be a sequence of independent identically distributed random variables with distribution function \(F(x)\), characteristic function \(f(t)\) and expectation \(EX_1\). Define the random walk \(S_n\) with steps \(X_1, X_2,\dots\) by \[ S_n= \sum^n_{i=1} X_i,\quad n= 1,2,\dots. \] Put \(N^+= \min\{n\mid S_n> 0\}\). (If the
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