Sojourn times. (1996) - Takács, Lajos
Abstract : Let ζ ( u ), u ≥ 0 be a stochastic process with state space A ∪ B 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. This article is dedicated to the memory of Roland L. Dobrushin.