Search results for "Absolute continuity"
showing 4 items of 34 documents
Statistical consequences of the Devroye inequality for processes. Applications to a class of non-uniformly hyperbolic dynamical systems
2005
In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functio…
On Variational Measures Related to Some Bases
2000
Abstract We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis.
On Descriptive Characterizations of an Integral Recovering a Function from Its $$L^r$$-Derivative
2022
The notion of Lr-variational measure generated by a function F ∈ Lr[a, b] is introduced and, in terms of absolute continuity of this measure, a descriptive characterization of the HKr -integral recovering a function from its Lr-derivative is given. It is shown that the class of functions generating absolutely continuous Lr-variational measure coincides with the class of ACGr -functions which was introduced earlier, and that both classes coincide with the class of the indefinite HKr-integrals under the assumption of Lr-differentiability almost everywhere of the functions consisting these classes
A Stieltjes Approach to Static Hedges
2014
Static hedging of complicated payoff structures by standard instruments becomes increasingly popular in finance. The classical approach is developed for quite regular functions, while for less regular cases, generalized functions and approximation arguments are used. In this note, we discuss the regularity conditions in the classical decomposition formula due to P. Carr and D. Madan (in Jarrow ed, Volatility, pp. 417–427, Risk Publ., London, 1998) if the integrals in this formula are interpreted as Lebesgue integrals with respect to the Lebesgue measure. Furthermore, we show that if we replace these integrals by Lebesgue–Stieltjes integrals, the family of representable functions can be exte…