  We utilize statistical tools to analyze the magnetic domain wall dynamics in
a nanostrip, which can quantify the magnitude and reveal the effects of
interfacial Dzyaloshinskii-Mariya interaction. We find that there exist two
peaks in the velocity frequency spectrum, the magnitude ratio of which can be
used to determine the DMI strength. Our approach is validated using a
collective-coordinate model, and is demonstrated to be robust against thermal
noise and material impurities. Moreover, third-order cumulant and third-order
time-dependent correlation function of velocity are calculated and yield
valuable information regarding the asymmetry induced by DMI. Our findings offer
novel and efficient analysis tools to understand physical process of domain
wall dynamics under DMI and exotic magnetic phenomena.
