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....

Stochastic complexity is treated as a tool of classification, i.e., of inferring the number of classes, the class descriptions, and the class memberships for a given data set of binary vectors. The stochastic complexity is evaluated with respect to the family of statistical models defined by...