Related papers: Kaminsky Type Functional Equations and Bivariate R…
We present an overview of the mathematical structure of geminal theory within the seniority formalism and bi-variational principle. Named after the constellation, geminal wavefunctions provide the mean-field like representation of…
A robust multilevel functional data method is proposed to forecast age-specific mortality rate and life expectancy for two or more populations in developed countries with high-quality vital registration systems. It uses a robust multilevel…
The limitations resulting from the dichtomisation of continuous outcomes have been extensively described. But the need to present results based on binary outcomes in particular in health science remains. Alternatives based on the…
We prove the existence of a weakly dependent strictly stationary solution of the equation $ X_t=F(X_{t-1},X_{t-2},X_{t-3},...;\xi_t)$ called {\em chain with infinite memory}. Here the {\em innovations} $\xi_t$ constitute an independent and…
This paper deals with the generalized convolutions connected with the Williamson transform and the maximum operation. We focus on such convolutions which can define transition probabilities of renewal processes. They should be monotonic…
Most present applications of time-dependent density functional theory use adiabatic functionals, i.e. the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go…
Frullani's integral dates from 1821, but a probabilistic interpretation of it has never been made. In this paper, Frullani's integral formula is shown to result from mixing a lifetime distribution by allowing the logarithm of the scale…
The pseudo-observations approach has been gaining popularity as a method to estimate covariate effects on censored survival data. It is used regularly to estimate covariate effects on quantities such as survival probabilities, restricted…
We develop a general formalism for the quantum kinetics of chiral fermions in a background electromagnetic field based on a semiclassical expansion of covariant Wigner functions in the Planck constant $\hbar$. We demonstrate to any order of…
Standard uniform convergence results bound the generalization gap of the expected loss over a hypothesis class. The emergence of risk-sensitive learning requires generalization guarantees for functionals of the loss distribution beyond the…
A multilevel functional data method is adapted for forecasting age-specific mortality for two or more populations in developed countries with high-quality vital registration systems. It uses multilevel functional principal component…
A binary operator * over real numbers is said to be associative if $(x*y)*z=x*(y*z)$ and is said to be reducible if $x*y=x*z$ or $y*w=z*w$ if and only if $z=y$. The operation is said to have an identity element $\tilde{e}$ if…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in Population Genetics, the so-called generalized Kimura diffusion operators. Our main results is a stochastic representation of…
We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem (Hara and Hino [Bull.\ London Math.\ Soc. \textbf{42}…
An elementary, but very useful lemma due to Biernacki and Krzy\.{z} (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of their respective coefficients. Over the last two decades it…
Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of…
Two stochastic representations of multivariate geometric distributions are analyzed, both are obtained by lifting the lack-of-memory (LM) property of the univariate geometric law to the multivariate case. On the one hand, the narrow-sense…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…