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Entrance from $$0+$$ for increasing semi-stable Markov processes. (English) Zbl 1002.60032
Let $$(X_t)_t$$ be an increasing semi-stable Markov process on the strict positive reals. J. Lampert [Z. Wahrscheinlichkeitstheorie Verw. Geb. 22, 205-225 (1972; Zbl 0274.60052)] gave a description via the Lévy processes. The main result here is: under a first moment condition, $$X(t)$$ converges weakly to some non-degenerate limit, as the starting point converges to $$0$$.
Reviewer: Uwe Rösler (Kiel)

##### MSC:
 60G18 Self-similar stochastic processes 60J50 Boundary theory for Markov processes 60G52 Stable stochastic processes