We study an information analogue of infinitely divisible probability distributions, where the i.i.d. sum is replaced by joint distribution sequence. A random variable $X$ called informationally if, for any notation="LaTeX">$n\ge 1$ , there exists sequence variables notation="LaTeX">$Z_{1},\ldots...

It is well-known that the following divisibility conditions are necessary for the existence of a t-(v, k, A) design: A(V-~) == 0 mod (k~), Os; i:::; t. t-, t-, A t.( v, k, A) design (0, £ilJ) with £ilJ =0 or ffi=Lk(n) is said to be trivial. One can show by elementary counting arguments that in a trivial t-(v, k,A) design, we must have either A=0 or A = (k=:)' The complement of a t.(v, k, A) des...

In this paper we introduce and study a regularising one-to-one mapping Υ0 from the class of one-dimensional Lévy measures into itself. This mapping appeared implicitly in our previous paper [BT2], where we introduced a one-to-one mapping Υ from the class ID(∗) of one-dimensional infinitely divisible probability measures into itself. Based on the studies of Υ0 in the present paper, we also deduc...

A probability measure μ on Rd is called weakly unimodal if there exists a constant κ ≥ 1 such that for all r > 0, (0.1) sup a∈Rd μ(B(a, r)) ≤ κμ(B(0, r)). Here, B(a, r) denotes the `∞-ball centered at a ∈ Rd with radius r > 0. In this note, we derive a sufficient condition for weak unimodality of a measure on the Borel subsets of Rd. In particular, we use this to prove that every symmetric infi...

The core of games arising from semi-infinite transportation situations with infinitely divisible goods is studied. In these situations one aims at maximizing the profit from transporting a good from a finite number of suppliers to an infinite number of demanders. This good is infinitely divisible. It is shown that the underlying primal and dual infinite programs have no duality gap. Further, th...

We extend the Lévy-Khintchine representation for an infinitely divisible distribution to define a driving process in the context of the bond price framework developed earlier. We describe a methodology using subordination to construct such processes and we develop some examples in detail.