The Ornstein–Uhlenbeck process Y started at x is a continuous Gaussian process with and covariance If X is the canonical process and Px is the law of an Ornstein–Uhlenbeck process started at x,...

The Ornstein–Uhlenbeck process Y started at x is a continuous Gaussian process with

and covariance

If X is the canonical process and Px is the law of an Ornstein–Uhlenbeck process started at x, show that

is a Markov process and determine the transition probabilities

Chapter 20