Nonlinearly perturbed regenerative processes and pseudo-stationary phenomena for stochastic systems

New types of mixed large deviation and ergodic theorems are obtained for nonlinearly perturbed regenerative processes, semi-Markov processes, and continuous-time Markov chains with absorption. Applications to the analysis of pseudo-stationary phenomena for stochastic systems are discussed. Examples related to models of population dynamics and highly reliable queuing systems are considered.