Exact expressions for moments of ladder heights (Q542288)

Let \((S_n)_{n\geq 0}\) be a zero-delayed random walk with i.i.d. increments. The paper provides explicit expressions for \(\operatorname{E}Z^m\), \(m\in\mathbb{N}\), where \(Z\) is the first ladder height. These expressions take different forms depending on whether \(\operatorname{E}S_1<0\), \(=0\), or \(>0\). Although the resulting formulae are complicated, they represent the moments of the ladder height in terms of the distribution of \(S_1\) which form the main achievement of the paper. Remark. The paper only announces results. No proofs are given.