Moments of last exit times for Ornstein-Uhlenbeck type Markov processes

Ornstein-Uhlenbeck process is widely used in the study of neuronal activity and in electricity markets spot price modeling. Let L_B be the last exit time from a compact set B of the Ornstein-Uhlenbeck type Markov process X = (Ω,ℱ, ℱ_t, X_t, θ_t, P^x) on R^d. A sufficient and necessary condition for E^x[L_B^η] <; ∞(η >; 0) is expressed in terms of transition probabilities of the process. Based on the condition, a criterion is given for E^x[L_B^η] <; ∞(η >; 0) using the Levy measure and the coefficient matrix of liner drift term which associate with the process.