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...

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_

Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Lévy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. We review their basic properties ...

We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable...

In a recent article Pillai (1990, Ann. Inst. Statist. Math., 42, 157-161) showed that the distribution 1-E~(-x~), 0 < c~ _< 1; 0 _< x, where E~(x) is the Mittag-Lettter function, is infinitely divisible and geometrically infinitely divisible. He also clarified the relation between this distribution and a stable distribution. In the present paper, we generalize his results by using Bernstein fun...

We give a proof of a theorem on the common divisibility of polynomials and permuted polynomials (over GF (2)) by a polynomial ( ).

We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t . We prove the first nontrivial degree formula and use it to show that existence of morphisms between algebraic varieties for which these numbers are not divisible by q give information on the degree of such morphisms or on zero c...

• Let R be a ring. Let u ∈ N and v ∈ N, and let ai,j be an element of R for every (i, j) ∈ {1, 2, ..., u} × {1, 2, ..., v} . Then, we denote by (ai,j) 1≤i≤u the u× v matrix A ∈ Ru×v whose entry in row i and column j is ai,j for every (i, j) ∈ {1, 2, ..., u} × {1, 2, ..., v} . • Let R be a commutative ring with unity. Let P ∈ R [X] be a polynomial. Let j ∈ N. Then, we denote by coeffj P the coef...

The self similar (fractal) structure of the Pascal triangle of binomial coefficients modulo some fixed prime has been known for some time and explored in detail. It turns out that such a fractal structure is the common property arithmetical functions of two variables possessing a more general recursive relation (R) f(i,j) = af(i-l,j) + bf(i 1,j-1) where a and b are fixed integers. 'When a, b ar...