On some random densities for random maps

On Random Maps Correlated With Random Densities

“…Remarks 12. 1-The main result of this paper (Theorem 11) extends a previous result (Theorem 7) in our paper [6] where we have considered the particular case I = J and q ij = p i p j for all 1 ≤ i, j ≤ I, that is the marginals are identical and independent.…”

“…where P T i is the Frobeinus-Perron operator of the deterministic map T i . Notice that if the marginals (a i ) and (b j ) are identical and independent, the preceding result is proved (Theorem 7) in our paper [6].…”

“…For the following classical concepts, we refer the reader to the monographs [3], [4], [8], [12]. In fact, since the present paper is a generalization of our article [6], all preliminaries are taken from this paper.…”

“…For the following notions, we will refer to [1], [6], [11]. Let (Ω, F, P) and (E, B, ρ) be two probability spaces.…”