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We present a new method for simulating Markovian jump processes withtime-dependent transitions rates, which avoids the transformation of randomnumbers by inverting time integrals over the rates. It relies on constructing asequence of random time points from a homogeneous Poisson process, where thesystem under investigation attempts to change its state with certainprobabilities. With respect to the underlying master equation the methodcorresponds to an exact formal solution in terms of a Dyson series. Differentalgorithms can be derived from the method and their power is demonstrated for aset of interacting two-level systems that are periodically driven by anexternal field.

Attempt-time Monte Carlo: an alternative for simulation of stochastic jump processes with time-dependent transition rates