Displaying similar documents to “Strong law of large numbers for branching diffusions”

Branching brownian motion with an inhomogeneous breeding potential

J. W. Harris, S. C. Harris (2009)

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

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This article concerns branching brownian motion (BBM) with dyadic branching at rate || for a particle with spatial position ∈ℝ, where >0. It is known that for >2 the number of particles blows up almost surely in finite time, while for =2 the expected number of particles alive blows up in finite time, although the number of particles alive remains finite almost surely, for all time. We define the right-most particle, , to be the supremum of the spatial positions...

Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder

M. D. Jara, C. Landim (2008)

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

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For a sequence of i.i.d. random variables { : ∈ℤ} bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at (resp. +1) jumps to +1 (resp. ) at rate . We examine a quenched non-equilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond disorder { : ∈ℤ}. We prove that the position of the tagged...

Polynomial bounds in the Ergodic theorem for one-dimensional diffusions and integrability of hitting times

Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2011)

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

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Let be a one-dimensional positive recurrent diffusion with initial distribution and invariant probability . Suppose that for some >1, ∈ℝ such that ∀∈ℝ, and , where is the hitting time of . For such a diffusion, we derive non-asymptotic deviation bounds of the form ℙ(|(1/)0 ( ) d−()|≥)≤()(1/ /2)(1/ )(). Here bounded or bounded and compactly supported and ()=‖‖∞ when is bounded and ()=(||) when is...

Spectral gaps and exponential integrability of hitting times for linear diffusions

Oleg Loukianov, Dasha Loukianova, Shiqi Song (2011)

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

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Let be a regular continuous positively recurrent Markov process with state space ℝ, scale function and speed measure . For ∈ℝ denote +=sup≥ (], +∞[)(()−()), −=sup≤ (]−∞; [)(()−()). It is well known that the finiteness of ± is equivalent to the existence of spectral gaps of generators associated with . We show how these quantities appear independently in the study of the exponential moments of hitting times...

Continuous-time multitype branching processes conditioned on very late extinction

Sophie Pénisson (2011)

ESAIM: Probability and Statistics

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Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob -transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.

Refracted Lévy processes

A. E. Kyprianou, R. L. Loeffen (2010)

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

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Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Lévy processes. The latter is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation d =− { ...