Ornstein-Uhlenbeck path integral and its application (Q5937961)

A path integral for the Ornstein-Uhlenbeck process distorted by a potential \(V(x)\) is introduced. The paper contains detailed investigation of \(T\to \infty\) limit of the probability distribution of \(X[\omega ] = 1/T^\nu\int_0^T V(\omega(t)) dt\) for Ornstein-Uhlenbeck process \(\omega(t)\), with appropriate values of the exponent \(\nu\). Comparison of the results with those for the Wiener process in included.