Displaying similar documents to “Branching brownian motion with an inhomogeneous breeding potential”

Strong law of large numbers for branching diffusions

János Engländer, Simon C. Harris, Andreas E. Kyprianou (2010)

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

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Let be the branching particle diffusion corresponding to the operator +(2−) on ⊆ℝ (where ≥0 and ≢0). Let denote the generalized principal eigenvalue for the operator + on and assume that it is finite. When >0 and +− satisfies certain spectral theoretical conditions, we prove that the random measure {− } converges almost surely in the vague topology as tends to infinity. This result...

The unscaled paths of branching brownian motion

Simon C. Harris, Matthew I. Roberts (2012)

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

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For a set ⊂ [0, ∞), we give new results on the growth of the number of particles in a branching Brownian motion whose paths fall within . We show that it is possible to work without rescaling the paths. We give large deviations probabilities as well as a more sophisticated proof of a result on growth in the number of particles along certain sets of paths. Our results reveal that the number of particles can oscillate dramatically. We also obtain new results on the number of particles...

Fractional multiplicative processes

Julien Barral, Benoît Mandelbrot (2009)

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

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Statistically self-similar measures on [0, 1] are limit of multiplicative cascades of random weights distributed on the -adic subintervals of [0, 1]. These weights are i.i.d., positive, and of expectation 1/. We extend these cascades naturally by allowing the random weights to take negative values. This yields martingales taking values in the space of continuous functions on [0, 1]. Specifically, we consider for each ∈(0, 1) the martingale ( ) obtained when the weights...

Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited

Emmanuel Cépa, Dominique Lépingle (2010)

ESAIM: Probability and Statistics

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The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of interacting Brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). We prove...