Talk:Kolmogorov continuity theorem

The condition

$\forall t\geq 0,\ \mathbb {P} (X_{t}={\tilde {X}}_{t})=1$

means that $X$ is a modification of the sample continuous process ${\tilde {X}}$. (This condition is even weaker than assuming that $X$ is a modification of a process that has surely continuous paths.) But what we want here is that $X$ has a continuous version, that is, there exists a (sample) continuous process ${\tilde {X}}$ such that

$\mathbb {P} (X_{t}={\tilde {X}}_{t}\ \forall t\geq 0)=1.$

Probabble (talk) 15:03, 3 May 2008 (UTC)