Related papers: Parameter estimation for fractional birth and frac…
Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on the system size (corresponding to the number of products or customers undergoing the birth-death process) and thus vary every…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…
Several convenient methods for calculation of fractional absolute moments are given with application to heavy tailed distributions. We use techniques of fractional differentiation to obtain formulae for $E[|X-\mu|^\gamma]$ with $1<\gamma<2$…
Let U be an open set in R^d. We show that under a mild assumption on the richness of the generator a Feller process in U with (predictable) killing is a semimartingale. To this end we generalize the notion of semimartingales in a natural…
We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of…
Various indicators and measures of the real life procedures rise up as functionals of the quantile process of a parent random variable Z. However, Z can be observed only through a response in a linear model whose covariates are not under…
The paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotics for the probability of excursions of a re-scaled…
This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative…
This paper develops the asymptotic theory for parametric and nonparametric regression models when the errors have a fractional local to unity root (FLUR) model structure. FLUR models are stationary time series with semi-long range…
In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the…
Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at…
We propose a framework for fitting fractional polynomials models as special cases of Bayesian Generalized Nonlinear Models, applying an adapted version of the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The…
This paper presents three fractional models formulated from a classical Pharmacokinetics compartmental system: commensurable, non-commensurable, and implicit non-commensurable models. Their distinguishing characteristics are further…
The dynamics of fermion generations is treated in the framework of the fractional Lagrangian and Hamiltonian in the compact extra dimension. The resulting spectra for u, d, e generations are described by the only mass parameter and slightly…
Suppose $M$ is a finite simplicial complex and that for $0=t_0,t_1,...,t_r=1$ we have a discrete Morse function $F_{t_i}:M\to \zr$. In this paper, we study the births and deaths of critical cells for the functions $F_{t_i}$ and present an…
\noindent The modal age at death is an increasingly used measure for understanding longevity and mortality patterns. However, existing estimation methods focus on point estimates, overlooking the inherent variability and uncertainty in…
Single-cell lineage tracking strategies enabled by recent experimental technologies have produced significant insights into cell fate decisions, but lack the quantitative framework necessary for rigorous statistical analysis of mechanistic…
We show that it is possible to replace the actual implicit distribution function of the fractional exclusion statistics by an explicit one whose form does not change with the parameter $\alpha$. This alternative simpler distribution…
We consider two non-linear generalizations of fractal interpolating functions generated from iterated function systems. The first corresponds to fitting data using a Kth-order polynomial, while the second relates to the freedom of adding…