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We analyze fluctuations of random walks with generally distributedincrements. Integral representations for key performance measures are obtainedby extending an inversion theorem of Hewitt [11] for Laplace-Stieltjestransforms. Another important part of the anal- ysis involves the so-calledharmonic measures associated to the distribution of the increment of the walk.It is also pointed out that such representations can be explicitly calculated,if one assumes a form of rational structure for the increment transform.Applications include, but are not restricted to, queueing and insurance riskproblems.

An extension of Hewitt's inversion formula and its application to fluctuation theory