The estimation for the distribution of residence time under interval objective domain

The distribution of the system output residence time under interval objective domain was researched for a normal stationary ergodic 1-dimension random process with discrete time. The sample space of system output was partitioned into many small intervals, and the small intervals outside of the objective were regarded as absorption state. Among these small intervals, the probability transition matrices, including the faster transition probability matrix and slower transition probability matrix, were established. Then these matrices were used to compute the probability distribution with controllable error. Then the conclusion that the relation among residence time (or mean residence time), variance and correlation coefficient is deterministic function was obtained. Therefore, the constrains for the residence time and its characteristic quantity can be changed to the constrains for the variance and the correlation coefficient. At last, an illustrative numerical example demonstrates the relation between the partitioned small intervals and the error.