A <càdlàg modification> of a <stochastic process> is a <modification of a stochastic process> whose paths are <càdlàg> on one event of probability one. Equality <almost surely> at every separately fixed time does not imply <indistinguishability of stochastic processes> when the original process lacks path regularity. A <stochastic process> starting at zero, with <independent increments>, <stationary increments>, and <stochastic continuity>, has a <càdlàg modification> and is a <Lévy process> under the intrinsic definition.


 Càdlàg modification (source code)