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The number of absorbed individuals in branching brownian motion with a barrier

Pascal Maillard (2013)

Annales de l'I.H.P. Probabilités et statistiques

We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift c . At the point x g t ; 0 , we add an absorbing barrier, i.e. individuals touching the barrier are instantly killed without producing offspring. It is known that there is a critical drift c 0 , such that this process becomes extinct almost surely if and only if c ≥ c 0 . In this case, if Z x denotes the number of individuals absorbed at the barrier, we give an asymptotic for P ( Z x = n ) as n goes to infinity. If c = c 0 ...

The Poisson boundary of random rational affinities

Sara Brofferio (2006)

Annales de l’institut Fourier

We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all p -adic fileds.

The Powers sum of spatial CPD-semigroups and CP-semigroups

Michael Skeide (2010)

Banach Center Publications

We define spatial CPD-semigroups and construct their Powers sum. We construct the Powers sum for general spatial CP-semigroups. In both cases, we show that the product system of that Powers sum is the product of the spatial product systems of its factors. We show that on the domain of intersection, pointwise bounded CPD-semigroups on the one side and Schur CP-semigroups on the other, the constructions coincide. This summarizes all known results about Powers sums and generalizes them considerably....

The rate of convergence for iterated function systems

Maciej Ślęczka (2011)

Studia Mathematica

Iterated function systems with place-dependent probabilities are considered. It is shown that the rate of convergence of transition probabilities to a unique invariant measure is geometric.

The renormalization transformation for two-type branching models

D. A. Dawson, A. Greven, F. den Hollander, Rongfeng Sun, J. M. Swart (2008)

Annales de l'I.H.P. Probabilités et statistiques

This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting within colonies. Their large-scale space–time behavior can be studied by means of a renormalization program. This program, which has been carried out successfully in a number of other cases (mostly one-dimensional), is based on the construction and the analysis of...

The risk-sensitive Poisson equation for a communicating Markov chain on a denumerable state space

Rolando Cavazos-Cadena (2009)

Kybernetika

This work concerns a discrete-time Markov chain with time-invariant transition mechanism and denumerable state space, which is endowed with a nonnegative cost function with finite support. The performance of the chain is measured by the (long-run) risk-sensitive average cost and, assuming that the state space is communicating, the existence of a solution to the risk-sensitive Poisson equation is established, a result that holds even for transient chains. Also, a sufficient criterion ensuring that...

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