Stochastic system behaviour described as a semigenerating process

A number of characteristics are given of a semigenerating process $Z$ such as distribution of $Z$ stay in a fixed region $A$, probability of $Z$ being in $A$ at time $t$, distribution of the number of $Z$ entering $A$ during period $[0, t]$, and $Z$, time of stay in $A$ over the period $[0, t]$. Limit relations as $t\to\infty$ are investigated. Examples are given which ishow effectiveness of using the results.