The Number of Phases of Inhomogeneous Markov Fields with Finite State Spaces on N and Z and their Behaviour at Infinity
✍ Scribed by Gerhard Winkler
- Publisher
- John Wiley and Sons
- Year
- 1981
- Tongue
- English
- Weight
- 848 KB
- Volume
- 104
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
GERHARD WINKLER of Miinchen
(Eingegsngen am 30. 13. 1980) .ibstract. We consider the set of noiilioniogeneous MARKOV fields on T = N o r T =Z with finite .Itate spaces E,, nET, with fixed local characteristics. For T = N we show that has at most iV-=lim inf lEnl phases. If T=Z, has a t most N-, . N-phases, wIiereN-,=linl inflEnl. We give examples, t h a t for T = N for any number i'c, 1 s k a N -, there are local characteristics with k phase8, whereas for I ' = Z every number I k, 1 s Z S N -~, 1 S k S Xoccurs. We describe the inner structure of q, the behaviour a t infinity and the connection between the one-sided and the twosided tail-fields. Simple examples of Markov fields which are no MARKOV processes are given.