  Skyrmions recently discovered in chiral magnets are a promising candidate for
magnetic storage devices because of their topological stability, small size
($\sim 3-100$nm), and ultra-low threshold current density ($\sim
10^{6}$A/m$^2$) to drive their motion. However, the time-dependent dynamics has
hitherto been largely unexplored. Here we show, by combining the numerical
solution of the Landau-Lifshitz-Gilbert equation and the analysis of a
generalized Thiele's equation, that inertial effects are almost completely
absent in skyrmion dynamics driven by a time-dependent current. In contrast,
the response to time-dependent magnetic forces and thermal fluctuations depends
strongly on frequency and is described by a large effective mass and a (anti-)
damping depending on the acceleration of the skyrmion. Thermal diffusion is
strongly suppressed by the cyclotron motion and is proportional to the Gilbert
damping coefficient $\alpha$. This indicates that the skyrmion position is
stable, and its motion responds to the time-dependent current without delay or
retardation even if it is fast. These findings demonstrate the advantages of
skyrmions as information carriers.
