New Limiting Distributions for Bellman-Harris Processes

New Limiting Distributions for Bellman–harris Processes

We present a number of new solutions to an integral equation arising in the limiting theory of Bellman–Harris processes. The argument proceeds via straightforward analysis of Mellin transforms. We also derive a criterion for the analyticity of the Laplace transform of the limiting distribution on Re(u) ≥ −c for some c > 0.

Limiting Distributions for Branching Processes

Limiting Conditional Distributions for Birth-death Processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on wheth...

Reconstruction of the Bellman-Harris branching

Consider the single-species, independent-particle, Bellman-Harris 9 branching process, defined by a progeny number distribution, and a particle 10 lifetime distribution. In this paper, we explore the existence and uniqueness of 11 the inverse problem, where one wishes to solve for the progeny number or lifetime 12 distribution given information about the total number distribution. Results 13 ar...

Bellman Processes

This morphism sends probability calculus into optimal control problems. Therefore almost of the concepts introduced in probability calculus have an optimization counterpart. The purpose of this paper is to make a presentation of known and new results of optimal control with this morphism in mind. The emphasis of this talk is i) on the trajectory point of view by opposition to the cost point of ...