ISSN:
1436-5081
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetP be a Markov process on a probability space (X, Σ,m). Roughly speaking, a sweep-out set is a set which is reached with probability 1 under the action of the process form-almost all starting points. Obviously, in a finite state space no sweep-out sets of arbitrary small measure exist. The authors show that in general arbitrary small sweep-out sets exist, unless there is an invariant subset of the state space on which the process behaves as on a finite state space. Moreover, if there exist arbitrary small sweep-out sets and if Σ is countably generated, then there exists an algebra of sweepout sets generating Σ. The main tool to obtain these results is the use of embedded processes. Some properties of these processes are collected, and as a side-result a short and elementary proof of the decomposition theorem ofE. Hopf of the state space in a conservative and a dissipative part is given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01300246
