Aldous tightness criterion
= Aldous tightness criterion
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For càdlàg processes on a finite horizon, compact containment together with uniformly small increments over pairs of bounded <stopping times> whose separation tends to zero is a sufficient criterion for tightness in the <Skorokhod J1 topology>. The increment condition is in probability, not merely at deterministic times. If in addition the largest jump tends to zero in probability, every limiting law is supported on continuous paths.