 Modification of a stochastic process

Processes $X,Y$ on the same probability space and index set are modifications of each other if $\mathbb{P}(X_t=Y_t)=1$ for each fixed index $t$. This differs from indistinguishability of stochastic processes, which requires equality at all indices on a single event of probability one. Equality at a countable dense set upgrades to indistinguishability when both processes have continuous paths.