Modification of a stochastic process
= 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.