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We establish a strong law of large numbers for one-dimensionalcontinuous-time random walks in dynamic random environments under two mainassumptions: the environment is required to satisfy a decoupling inequalitythat can be interpreted as a bound on the speed of dependence propagation,while the random walk is assumed to move ballistically with a speed larger thanthis bound. Applications include environments with strong space-timecorrelations such as the zero-range process and the asymmetric exclusionprocess.

Law of large numbers for ballistic random walks in dynamic random environments under lateral decoupling