Let $X_1, X_2,\ldots X_n$ be $n$ samples taken of a random variable with a given distribution (so in particular it is i.i.d.). Is there literature on or a name for the random variable defined by $$Y = \sum_{i=1}^{n-1}\left|X_i-X_{i+1}\right|?$$
If necessary feel free to add further assumptions, such as $X_i$ being non-negative, or the $X_i$ being drawn from specific distributions.