Abstract
Let X,X 1,X 2, … be independent identically distributed random variables, F(x) = P{X < x}, S 0 = 0, and S n =Σ =1 X i . We consider the random variables, ladder heights Z + and Z − that are respectively the first positive sum and the first negative sum in the random walk {S n }, n = 0, 1, 2, …. We calculate the first three (four in the case EX = 0) moments of random variables Z + and Z − in the qualitatively different cases EX > 0, EX < 0, and EX = 0.
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