Sample-continuous process
In mathematics, a sample-continuous process is a stochastic process whose sample paths are almost surely continuous functions.Definition
Let be a probability space. Let X : I × Ω → S be a stochastic process, where the index set I and state space S are both topological spaces. Then the process X is called sample-continuous if the map X : I → S is continuous as a function of topological spaces for P-almost all ω in Ω.
In many examples, the index set I is an interval of time, or 0, +∞), and the state space S is the [real line or n-dimensional Euclidean space Rn.Examples
