A note on generalized CIR equations

The note is a complement to the paper [M. Barski and J. Zabczyk, “On CIR equations with general factors”, SIAM Journal on Financial Mathematics 11, No. 1, 131–147] by the authors on the generalized CIR equation. We provide here a stochastic analysis proof of a crucial step of the proof in that paper which required there some advanced results on infinitesimal generators of a class of Markov processes.