Infinitely divisible sequences and renewal sequences

Multivariate geometric distributions with limited memory, d-monotone sequences, and infinitely divisible laws

In this talk we discuss and characterize multivariate geometric distributions with lack-of-memory (LM) property. First, a multivariate extension of the univariate geometric law is derived using a discrete analogue of the Marshall-Olkin exponential “shock model”. It is shown that only the subclass of multivariate LM distributions with positively correlated components can be obtained in this way....

A characterization of m-dependent stationary infinitely divisible sequences with applications to weak convergence

m-dependent stationary infinitely divisible sequences are characterized as a certain generalized finite moving average sequence or equivalently via the structure of their Lévy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of m-dependent stationary infinitely divisible sequences. Partial sum con...

Infinitely Divisible Matrices

Infinitely divisible cascades

Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic, to name but two. It was recently shown and explained how and why multifractal analysis could be interestingly and fruitfully placed in the more general framework of infinitely divisible cascades. The aim of this contribution is to design processes, c...

Unbounded Regions of Infinitely Logconcave Sequences

We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that is ∞-logconcave. This problem was motivated by the conjecture of Moll and Boros in [1] that the binomial coefficients are ∞-logconcave.