IX: 23, 443-463, LNM 465 (1975)
GETOOR, Ronald K.
On the construction of kernels (
Measure theory)
Given two measurable spaces $(E, {\cal E})$ $(F, {\cal F})$ and a family ${\cal N}\subset{\cal E}$ of negligible sets, a pseudo-kernel $T$ is a mapping from bounded measurable functions on $F$ to classes mod.${\cal N}$ of bounded measurable functions on $E$, which has all a.e. the properties (positivity, countable additivity) of a kernel. Regularizing $T$ consists in finding a true kernel $\hat T$ such that $\hat Tf$ belongs to the class $Tf$ for every measurable bounded $f$ on $F$. The regularization is easy whenever $F$ is compact metric. Then the result is extended to the case of a Lusin space, and to the case of a U-space (Radon space) assuming ${\cal N}$ consists of the negligible sets for a family of measures on $E$. An application is given to densities of continuous additive functionals of a Markov process
Comment: The author states that his paper is purely expository. This is not true, though the proof is a standard one in the theory of conditional distributions. For a deeper result, see Dellacherie
1030. For a presentation in book form, see Dellacherie-Meyer,
Probabilités et Potentiel C, chapter XI
41Keywords: Pseudo-kernels,
RegularizationNature: Original
Retrieve article from Numdam
XII: 27, 398-410, LNM 649 (1978)
GETOOR, Ronald K.
Homogeneous potentials (
General theory of processes)
This is a development in Knight's prediction theory as described in
1007,
1008. Let $(Z_t^\mu)$ be the prediction process associated with a given measure $\mu$. Then it is shown that a bounded homogeneous right continuous supermartingale (or potential) under $\mu$ remains so under the measures $Z_t^\mu$
Keywords: Prediction theoryNature: Original Retrieve article from Numdam
XIV: 42, 397-409, LNM 784 (1980)
GETOOR, Ronald K.
Transience and recurrence of Markov processes (
Markov processes)
From the introduction: The purpose of this paper is to present an elementary exposition of some various conditions that have been used to define transience or recurrence of a Markov process... an elementary and unified discussion of these ideas may be worthwhile
Keywords: Recurrent Markov processesNature: Exposition,
Original additions Retrieve article from Numdam
XXVI: 34, 485-497, LNM 1526 (1992)
FITZSIMMONS, Patrick J.;
GETOOR, Ronald K.
Some applications of quasi-boundedness for excessive measures Retrieve article from Numdam
