Summary
The aim of this paper is the construction of a class of semi-groups of homogeneous onedimensional Markov processes with respect to a given infinitesimal operator. This is done namely by the method of stochastic integration represented in the book of Skorokhod. The Lipschitzian conditions — needed there — are weakened to uniform continuity by a method of approximation of semi-groups. Also to these semi-groups we can construct Markov processes as solutions of stochastic integral equations. The representation is connected with the result of Meyer, Watanabe, Motoo.
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Literatur
Meyer, P.A.: Intégrales Stochastiques. Strasbourg: Séminaire de Probabilité 1966/67.
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Eifrig, B. Zur Konstruktion eindimensionaler homogener Markoffscher Prozesse. Z. Wahrscheinlichkeitstheorie verw Gebiete 14, 127–139 (1969). https://doi.org/10.1007/BF00537518
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DOI: https://doi.org/10.1007/BF00537518