A general construction for ?nite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of f n () will imply the existence of a ?nite invariant measure for the map f which is absolutely continuous with respect to , a measure on the phase space describing the sets of measure zero. Furthermore we will discuss ...

The article focuses on mortality models with a random effect applied in order to evaluate human more precisely. Such are called frailty or Cox models. main assertion of the paper shows that each positive transforms initial hazard rate (or density function) new absolutely continuous survival function. In particular, well-known Weibull and Gompertz rates corresponding functions analyzed different...

Let S be the orthogonal sum of infinitely many pairwise unitarily equivalent symmetric operators with non-zero deficiency indices. Let J be an open subset of R. If there exists a self-adjoint extension S0 of S such that J is contained in the resolvent set of S0 and the associated Weyl function of the pair {S, S0} is monotone with respect to J , then for any self-adjoint operator R there exists ...

t− a if a ≤ t ≤ x t− b if x < t ≤ b . In the last decade, many authors (see for example [2] and the references therein) have extended the above result for different classes of functions defined on a compact interval, including: functions of bounded variation, monotonic functions, convex functions, n-time differentiable functions whose derivatives are absolutely continuous or satisfy different c...

Abstract. The Stieltjes–Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L-spaces. Under some additional assumptions these measures are exactly the solutions to the q-Pear...

A generalization of Émery’s inequality for stochastic integrals is shown for convolution integrals of the form ( ∫ t 0 g(t − s)Y (s−) dZ(s))t>0, where Z is a semimartingale, Y an adapted càdlàg process, and g a deterministic function. The function g is assumed to be absolutely continuous with a derivative that is continuous or of bounded variation or a sum of such functions. The function g may ...