Markoff-Ketten bei sich füllenden Löchern im Zustandsraum

Hermann Rost

Annales de l'institut Fourier (1971)

  • Volume: 21, Issue: 1, page 253-270
  • ISSN: 0373-0956

Abstract

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Given a substochastic kernel P from a measurable space ( E , β ) into itself one considers for a pair ( μ , ν ) of finite measures on β the following sequences: μ 0 = ( μ - ν ) + , ν 0 = ( μ - ν ) - ; μ n + 1 = ( μ n p - ν n ) + , ν n + 1 = ( μ n p - ν n ) - , n = 0 , 1 , 2 , ... This paper deals with conditions for ↓ lim n ν n = 0 , or lim n ∥ μ n ∥ = 0 to hold. As an application a characterization of those measures ν is given which may occur in a P -Markov chain ( X n ) n ∈ N with state space E , having μ as its initial law, as distribution of X τ where τ is a suitable stopping time.

How to cite

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Rost, Hermann. "Markoff-Ketten bei sich füllenden Löchern im Zustandsraum." Annales de l'institut Fourier 21.1 (1971): 253-270. <http://eudml.org/doc/74027>.

@article{Rost1971,
author = {Rost, Hermann},
journal = {Annales de l'institut Fourier},
keywords = {probability theory},
language = {ger},
number = {1},
pages = {253-270},
publisher = {Association des Annales de l'Institut Fourier},
title = {Markoff-Ketten bei sich füllenden Löchern im Zustandsraum},
url = {http://eudml.org/doc/74027},
volume = {21},
year = {1971},
}

TY - JOUR
AU - Rost, Hermann
TI - Markoff-Ketten bei sich füllenden Löchern im Zustandsraum
JO - Annales de l'institut Fourier
PY - 1971
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 1
SP - 253
EP - 270
LA - ger
KW - probability theory
UR - http://eudml.org/doc/74027
ER -

References

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  1. [1] M.A. AKCOGLU, R.W. SHARPE, Ergodic theory and boundaries, Trans. Amer. Math. Soc. 132 (1968), 447-460. Zbl0162.19402MR37 #369
  2. [2] R.V. CHACON, D.S. ORNSTEIN, A general ergodic theorem, III. Journal Math. 4 (1960), 153-160. Zbl0134.12102MR22 #1822
  3. [3] E.B. DYNKIN, A.A. JUSCHKEWITSCH, Sätze und Aufgaben über Markoffsche Prozesse, Berlin-Heidelberg-New York : Springer 1969. Zbl0196.19603
  4. [4] P.A. MEYER, Théorie ergodique et potentiels, Ann. Inst. Fourier 15 (1965), 89-102. Zbl0134.32402MR34 #308a
  5. [5] P.A. MEYER, Probabilités et potentiel, Paris : Hermann 1966. Zbl0138.10402MR34 #5118
  6. [6] H. ROST, Darstellung einer Ordnung von Massen durch Stoppzeiten, Z. Wahrscheinlichkeitstheorie verw. Geb. 15 (1970), 19-28. Zbl0192.53501MR43 #6973

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