For a distribution F * τ of a random sum S τ = ξ 1 +. .. + ξ τ of i.i.d. random variables with a common distribution F on the half-line [0, ∞), we study the limits of the ratios of tails F * τ (x)/F (x) as x → ∞ (here τ is an independent counting random variable). We also consider applications of obtained results to random walks, compound Poisson distributions, infinitely divisible laws, and su...

The goal of the paper is to show that some types of Lévy processes such as the hyperbolic motion and the CGMY are particularly suitable for asset price modelling and option pricing. We wish to review some fundamental mathematic properties of Lévy distributions, such as the one of infinite divisibility, and how they translate observed features of asset price returns. We explain how these process...

Blanchard and Fabre (1994) have considered description of symbolic systems by sequences obtained by iteration of two mappings $1, and d,, defined by g,(u) = u[u], and L/, J u[u]:, m here the word [u], is obtained from a word u by removing the last ,j symbols. They stated a conjecture thal the iteration of (I, results in an automatic sequence. We prove here that t/, ix. while (1) 1s not, a 2.aut...

This paper describes an algorithm to find an (a-)envy-free Pareto-optimal division in the case of a finite number of homogeneous infinitely divisible goods and linear utility functions. It is used to find an allocation in the classical cake division problem that is almost Pareto-op timat and o-envy-free. 9 1998 The Mathematical Pregraming, Society, Inc. Published by Elsevier Science B.V_

This paper is concerned with an investigation into the localized instability of a thin elastic orthotropic semi-infinite plate. In this study, a semi-infinite plate, simply supported on two edges and under different boundary conditions of clamped, hinged, sliding contact and free on the other edge, is studied. A mathematical model is used and a general solution is presented. The conditions unde...

For a distribution F * τ of a random sum S τ = ξ 1 +. .. + ξ τ of i.i.d. random variables with a common distribution F on the half-line [0, ∞), we study the limits of the ratios of tails F * τ (x)/F (x) as x → ∞ (here τ is an independent counting random variable). We also consider applications of obtained results to random walks, compound Poisson distributions, infinitely divisible laws, and su...

We consider adaptive periodic IIR ltering and present an extension of the Hyperstable Adaptive Recursive Filter (HARF). We give conditions for convergence of the parameter estimate error, involving passivity of certain operators in the identi cation loop, identi ability of the system parameters, and persistent excitation (pe). A necessary and su cient condition for identi ability is given and s...