Quasi-stationary distributions for continuous-time λ-recurrent jump processes

For the continuous-time λ-recurrent jump process, the λ-recurrence assures the existence of quasi-stationary distribution when it has finite exit states (the states that have positive killing rates). And we give an explicit representation for this quasi-stationary distribution through Q-matrix, where the components of the quasi-stationary distribution outside the set H of exit states can be represented by those within H. Sufficient condition is also provided for quasi-stationary distribution when the exit states are infinite.