|
|||||
|
|
|
|
|
|
|
|
|
Sample function
behavior of increasing processes with stationary, independent
increments
Bert E. Fristedt |
|
Vol. 21 (1967), No. 1, 21–33
|
Abstract |
|
In this paper we are concerned with the sample functions of increasing stochastic processes, Xν, having stationary, independent increments; normalized so that Xν has no deterministic linear component and Xν(0) = 0, (i.e., X∨ is a subordinator). For h a fixed function, we are interested in the following two events: { ω : Xν(t,ω) > h(t) infinitely often as t → 0}, { ω : Xν(t,ω) > h(t) infinitely often as t →∞}. In case Xν is a stable process, Khinchin has given integral tests to apply to a wide class of h′s in order to decide whether one, the other, or both of these two events have probability zero or one. The purpose of this paper is to give similar results, without assuming Xu to be stable. |
Mathematical Subject Classification
Primary: 60.60
|
Milestones
Received: 18 November 1965
Published: 1 April 1967
|
Authors |
| Bert E. Fristedt | |
|
