Before revision: In this paper, we show that the behaviors of price fluctuations in  cryptocurrency markets can also be characterized by a Levy's stable distribution  under certain conditions of time intervals ranging from 30 minutes to 4 hours.
After revision: In this paper, we show that the behaviors of price fluctuations in cryptocurrency markets can also be characterized by a Levy's stable distribution under certain conditions outside time intervals ranging from 30 minutes to 4 hours.