Ito process

Stability of the Ito Processes Set

Stability over addition

The sum of two Ito Processes is obviously another Ito Process

Stability over Integration

$\forall X\in {\mathcal {I}},\ {\mathcal {I}}\in {\mathcal {L}}(X)$. Which means that any Ito Process can be integrated with respect to any other Ito Process. Moreover, the Stochastic Integral with respect to an Ito Process is still an Ito Process.

This exceptional stability is one of the reasons of the wide use of Ito Processes. The other reason is the Ito Formula.