Convert Parametric SDE Processes to Equivalent Ito Processes

The canonical form of ItoProcess or StratonovichProcess in the Wolfram Language encodes their defining SDEs as follows:
WienerProcess solves the SDE , where is the standard Wiener process, also known as the Brownian motion process:
OrnsteinUhlenbeckProcess solves the SDE :
CoxIngersollRossProcess solves the SDE :
BrownianBridgeProcess solves the SDE :