Generalized Moments of Several Variables Related to Random Walks with Positive Drift
Yongcheng Qi · Acta Scicentiarum Naturalum Universitis Pekinesis · 1993
The sequence of partial sums of a sequence of i. i. d. random variables with positive expectation is considered in this paper. Some random quantities defined by the sequence of partial sums, e. g., the time at which the first or the last crossing of a given level occurs, the value of the partial sums immediately before or after the crosing, the minimum of all partial sums, are studied. The necessary and sufficient conditions for the existence of generalized moments of these quantities are proved.