Additive functionals and entrance laws

Representation of additive and biadditive functionals

Additive functionals and excursions of Kuznetsov processes

Let B be a continuous additive functional for a standard process (Xt)t∈R+ and let (Yt)t∈R be a stationary Kuznetsov process with the same semigroup of transition. In this paper, we give the excursion laws of (Xt)t∈R+ conditioned on the strict past and future without duality hypothesis. We study excursions of a general regenerative system and of a regenerative system consisting of the closure of...

Additive functionals on multiway search trees

We derive asymptotics of moments and limiting distributions, under the random permutation model on m-ary search trees on n keys, of functionals that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal path length, and the socalled shape functional fall under this framework. The limiting behavior of these functionals exhibi...

Additive Functionals of Infinite-variance Moving Averages

We consider the asymptotic behavior of additive functionals of linear processes with infinite variance innovations. Applying the central limit theory for Markov chains, we establish asymptotic normality for short-range dependent processes. A non-central limit theorem is obtained when the processes are long-range dependent and the innovations are in the domain of attraction of stable laws.

Characterizing neuromorphologic alterations with additive shape functionals

The complexity of a neuronal cell shape is known to be related to its function. Specifically, among other indicators, a decreased complexity in the dendritic trees of cortical pyramidal neurons has been associated with mental retardation. In this paper we develop a procedure to address the characterization of morphological changes induced in cultured neurons by over-expressing a gene involved i...