Sojourn times. (1996)

• Record Type: Journal Article
• Authors: Takács, Lajos
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 4(1996)
• Page Start: 415
• Page End: 426
• Publication Date: 1996
• Subjects: stochastic processes -- Sojourn times -- distributions -- limit distributions; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000366
• Languages: English
• ISSNs: 1048-9533

Abstract

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.