The Ornstein–Uhlenbeck operator is clearly stated in the link below. https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_operator In the link it is also stated that "not to be confused with Ornstein–Uhlenbeck Process"
The question is why the the operator is named after them? Why it is called by the name "Ornstein–Uhlenbeck operator"? Is there a connection between the process and the operator, could not find one. Any suggestion?
They are closely connected. The operator is the infinitesimal generator of the process.