Geodesic
A note on integral representation of Feller kernels
Annales Polonici Mathematici, Tome 56 (1991) no. 1, pp. 93-96

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We consider integral representations of Feller probability kernels from a Tikhonov space X into a Hausdorff space Y by continuous functions from X into Y. From the existence of such a representation for every kernel it follows that the space X has to be 0-dimensional. Moreover, both types of representations coincide in the metrizable case when in addition X is compact and Y is complete. It is also proved that the representation of a single kernel is equivalent to the existence of some non-direct product measure on the product space $Y^ℕ$.
DOI : 10.4064/ap-56-1-93-96
Keywords: Feller kernel, integral representation

R. Rębowski 1

1 
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R. Rębowski. A note on integral representation of Feller kernels. Annales Polonici Mathematici, Tome 56 (1991) no. 1, pp. 93-96. doi: 10.4064/ap-56-1-93-96

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