Nonpositivity of Markov chains with increasing oscillations. (English. Ukrainian original) Zbl 0923.60081

Filonov, Yu. P.

Theory Probab. Math. Stat. 56, 81-85 (1998); translation from Teor. Jmovirn. Mat. Stat. 56, 81-86 (1997).

Let \(P(x,y)\) be a transition probability of an irreducible Markov chain with a general phase space. The famous criterion of nonpositivity uses the equality \(\int | f(y)-f(x)| P(x,dy)=O(1)\). The author gives a general criterion (Theorem 1) which uses a weaker condition than that mentioned above. Applying this condition to the special classes of chains the author shows (Theorems 2 and 3) that sometimes the traditional criterion does not work but the proposed one gives all classes of nonpositivity.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60J05	Discrete-time Markov processes on general state spaces
60J45	Probabilistic potential theory
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

irreducible Markov chain; nonpositivity condition