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THE SUM OF THE RECIPROCAL OF THE RANDOM WALK

Jon Michel and Robert de Jong

Econometric Theory, 2020, vol. 36, issue 1, 170-183

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.

Date: 2020
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