= Sample path
{title2=$t\mapsto X_t(\omega)$}
= Sample trajectory
{synonym}
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.
Back to article page
