 Sample path

For a stochastic process $X_t$ and a fixed sample outcome $\omega$, its sample path is the function $t\mapsto X_t(\omega )$. Statements about continuous, càdlàg or Hölder continuous function sample paths concern these functions simultaneously in time; they differ from assertions made only at each fixed deterministic time. A probability-one path property can be checked using countable dense times when the appropriate continuity is available.