THE SUM OF THE RECIPROCAL OF THE RANDOM WALK. (February 2020) - Michel, Jon; de Jong, Robert
Abstract : This paper derives the limit distribution of the rescaled sum of the reciprocal of the positive part of a random walk with continuously distributed innovations, and of the rescaled sum of the reciprocal of the absolute value of a random walk with continuously distributed innovations. It also considers this statistic for the case of a simple random walk, and shows that the limit distribution is different for this case.