Densities for infinitely divisible random processes

Let {ξ_j(t), t ∈ [0, T]} j = 1, 2 be infinitely divisible processes with distinct Poisson components and no Gaussian components. Let X be the set of all real-valued functions on [0, T] which are not identically zero, and $\text{B}$ be the σ-ring generated by the cylinder sets of ξ_j(t), j = 1, 2. Let μ_j be the measure on $\text{B}$ induced by ξ_j(t).Necessary and sufficient conditions on the projective limits of the Levy-Khinchine spectral measures of the processes are found to make μ₂ ? μ₁, and a representation for the density $\text{dμ}{}_2\text{dμ}{}_1$ is obtained.     

On infinitely divisible self-similar random fields

Summary A class of self-similar stationary random fields in ^d , d1 with finite variance is constructed by means of multiple stochastic integrals with respect to the Poisson random measure in ^d+1. Various topics associated with these fields such as subordination, ergodicity, existence of higher order moments, uniqueness of stochastic integral representation, renormalized powers of linear generalized fields and some limit theorems are studied. A Lévy-Hinin type formula for the characteristic functional of general infinitely divisible self-similar random fields with finite variance is obtained.     

An inverse problem for infinitely divisible moving average random fields

Statistical Inference for Stochastic Processes - Given a low frequency sample of an infinitely divisible moving average random field $${int _{mathbb {R}^d} f(x-t)varLambda (dx); t in mathbb...     

Weak convergence of martingales with random indices to infinitely divisible laws

Acta Mathematica Hungarica -     

Characterization of palm distributions and infinitely divisible random measures

The purpose of the present paper is to characterize Campbell measures and Palm distributions of random measures and to apply these results in a new approach to the characterizations of infinitely divisible random measures by their Laplace functionals and their Palm distributions. The results on infinitely divisible random measures are well known. They can be found together with a detailed list of references in Kallenberg's monograph [2], which also contains proofs of almost all statements in Section 1 of this paper (see his note on page 9 concerning the Polish space setting).     

Structure of exchangeable infinitely divisible sequences of poisson random vectors

De Finetti's Theorem reveals a simple explicit structure for an infinite exchangeable sequence of zero-one random variables. Although more general results are known, simple explicit results might be expected in particular settings. In this paper such results are obtained for exchangeable sequences of infinitely divisible Poisson random variables and random vectors. The methods employed are elementary, except in that they involve appeal to moment theorems.     

Testing independence of variates in an infinitely divisible random vector

A method is given for testing the independence of variates in an infinitely divisible random vector and for testing the independence of several subsets of the variates. Applications to stochastic processes are indicated.     

A class of infinitely divisible distributions connected to branching processes and random walks

A class of infinitely divisible distributions on {0,1,2,…} is defined by requiring the (discrete) Lévy function to be equal to the probability function except for a very simple factor. These distributions turn out to be special cases of the total offspring distributions in (sub)critical branching processes and can also be interpreted as first passage times in certain random walks. There are connections with Lambert's W function and generalized negative binomial convolutions.     

Some sufficient conditions for a finite group to be supersolvable

This paper represents an attempt to extend and improve the following result of Berkovich: Let G be a group of odd order. Let G=G ₁ G ₂ such that G ₁ and G ₂ are subgroups of?G. If the Sylow p-subgroups of G ₁ and of G ₂ are cyclic, then G is p-supersolvable.     

Necessary and sufficient conditions for a penalty method to be exact

This paper identifies necessary and sufficient conditions for a penalty method to yield an optimal solution or a Lagrange multiplier of a convex programming problem by means of a single unconstrained minimization. The conditions are given in terms of properties of the objective and constraint functions of the problem as well as the penalty function adopted. It is shown among other things that all linear programs with finite optimal value satisfy such conditions when the penalty function is quadratic.     

Necessary and sufficient conditions for a graph to be three-terminal series-parallel-cascade

A “three-terminal series-parallel-cascade graph” is defined as a three-terminal graph which is constructed by means of cascade connections in addition to series and parallel connections which were used in constructing a three-terminal series-parallel graph in our previous paper. Some properties of the graph are presented, and a theorem of the Kuratowski type is given stating that a three-terminal nonseparable graph is three-terminal series-parallel-cascade if and only if none of certain three graphs can be obtained from it by opening or shorting some of the edges. This theorem characterizes a three-terminal series-parallel-cascade graph completely, and clarifies its structual limitation.