Sojourn times

Let {ω(u),u≥0} be a stochastic process with state space AℝB where A and B are disjoint sets. Denote by β(t) the total time spent in state B in the interval (0,t). This paper deals with the problem of finding the distribution of β(t) and the asymptotic distribution of β(t) as t⇒• for various types of stochastic processes. The main result is a combinatorial theorem which makes it possible to find in an elementary way, the distribution of β(t) for homogeneous stochastic processes with independent increments.