Approximations in bivariate renewal theory

A Bivariate Renewal Process and Its Applications in Maintenance Policies

Renewal Theory

(1) Sn = S0 + n ∑ i=1 Xi When S0 = 0 the renewal process is an ordinary renewal process; when S0 is a nonnegative random variable the renewal process is a delayed renewal process. In either case, the individual terms Sn of this sequence are called renewals, or sometimes occurrences. With each renewal process is associated a renewal counting process N (t ) that tracks the total number of renewal...

Theory of Bivariate Ace

Recently, L. Breiman and l.R. Friedman introduced a non-parametric method for estimating transformations in regression data, the so called ACE-algorithm. This method promises to become one of the most powerful tools in data analysis, if some pitfalls are avoided. We point out some unexpected features in ACE as well as some curiosities in its mathematics which relate to tomography and projection...

Selfconsistent Approximations in Mori’s Theory

The constitutive quantities in Mori’s theory, the residual forces, are expanded in terms of time dependent correlation functions and products of operators at t = 0, where it is assumed that the time derivatives of the observables are given by products of them. As a first consequence the Heisenberg dynamics of the observables are obtained as an expansion of the same type. The dynamic equations f...

Cycle Factors and Renewal Theory

For which values of k does a uniformly chosen 3-regular graph G on n vertices typically contain n/k vertex-disjoint k-cycles (a k-cycle factor)? To date, this has been answered for k = n and for k logn; the former, the Hamiltonicity problem, was finally answered in the affirmative by Robinson and Wormald in 1992, while the answer in the latter case is negative since with high probability (w.h.p...