  The thermal stability in nanostructured magnetic systems is an important
issue for applications in information storage. From a theoretical and
simulation perspective, an accurate prediction of thermally-activated
transitions is a challenging problem because desired retention times are on the
order of 10 years, while the characteristic time scale for precessional
magnetization dynamics is of the order of nanoseconds. Here, we present a
theoretical study of the thermal stability of magnetic elements in the form of
perpendicularly-magnetized ferromagnetic disks using the forward flux sampling
method, which is useful for simulating rare events. We demonstrate how rates of
thermally-activated switching between the two uniformly-magnetized ``up'' and
``down'' states, which occurs through domain wall nucleation and propagation,
vary with the interfacial Dzyaloshinskii-Moriya interaction, which affect the
energy barrier separating these states. Moreover, we find that the average
lifetimes differ by several orders of magnitude from estimates based on the
commonly assumed value of 1 GHz for the attempt frequency.
