On the Existence of Invariant Measures for Piecewise Monotonic Transformations

New dependence coefficients. Examples and applications to statistics

“…In many interesting cases, the spectral analysis of L in the Banach space of BV -functions equiped with the norm h v = dh + h 1,λ can be done by using the Theorem of Ionescu-Tulcea and Marinescu (see Lasota and Yorke (1974) and Hofbauer and Keller (1982)). Assume that 1 is a simple eigenvalue of L and that the rest of the spectrum is contained in a closed disk of radius strictly smaller than one.…”

Absolutely continuous invariant measures for expanding piecewise linear maps

“…Moreover, we find that the sufficient condition is also useful for piecewise linear maps. In fact, we do not know whether the results in this paper can be obtained by using bounded variation functions in the sense of distributions, which has been used in the papers [1,7,[12][13][14]16]. The second one is that of the weighted multiplicity.…”

“…where U v is the domain of definition given by (14). Let m be the set of combinations v as (20) such that D v T is defined and that the vectors…”

“…In 1973, Lasota and Yorke proved the existence of an absolutely continuous invariant probability measure for every expanding piecewise C 2 map on bounded intervals [14]. This is the origin of the argument on the existence or non-existence of absolutely continuous invariant measures for piecewise expanding maps.…”

The β α-Encoders for Robust A/D Conversion

“…In [5], Lasota and Yorke proved that under these conditions there exist at least one nonnegative function f of bounded variation such that the measure μ with dμ = f dm (where m is the Lebesgue measure) is invariant under T , in the sense that…”