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.