On the Integral Equation of Renewal Theory

  title={On the Integral Equation of Renewal Theory},
  author={David P. Smith and Nathan Keyfitz},
Feller’s paper is a rigorous treatment of renewal theory, and to assist the reader his principal results are summarized below in demographic form and notation. 

Nonlinearly Perturbed Renewal Equations : asymptotic Results and Applications

In this thesis we investigate a model of nonlinearly perturbed continuous-time renewal equation. Some characteristics of the renewal equation are assumed to have non-polynomial perturbations, more ...

Measure solutions to the conservative renewal equation

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Piecewise orthogonal collocation for computing periodic solutions of renewal equations

We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence


  • P. Brill
  • Mathematics
    Probability in the Engineering and Informational Sciences
  • 2014
We introduce a level-crossing analysis of the finite time-t probability distributions of the excess life, age, total life, and related quantities of renewal processes. The technique embeds the

Fractional order error estimates for the renewal density

. We study the rate of convergence for the renewal density with the interarrival times that are absolutely continuous, not necessarily positive, and has finite moment of α th order with α > 3 / 2. We

Spectral Approximation of Convolution Operators

We develop a unified framework for constructing matrix approximations to the convolution operator of Volterra type defined by functions that are approximated using classical orthogonal polynomials ...

On a class of neutral equations with state-dependent delay in population dynamics

We introduce a new class of nonlinear neutral functional differential equations (NFDEs) with state-dependent delay. An extension of the existing theory for NFDEs is provided, allowing for results on