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Large scale behaviour of the spatial $𝛬$ -Fleming–Viot process

N. Berestycki, A. M. Etheridge, A. Véber (2013)

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

We consider the spatial $𝛬$ -Fleming–Viot process model (Electron. J. Probab.15(2010) 162–216) for frequencies of genetic types in a population living in $ℝ^{d}$ , in the special case in which there are just two types of individuals, labelled $0$ and $1$ . At time zero, everyone in a given half-space has type 1, whereas everyone in the complementary half-space has type $0$ . We are concerned with patterns of frequencies of the two types at large space and time scales. We consider two cases, one in which the dynamics...

Laws of the iterated logarithm for the brownian snake

Laurent Serlet (2000)

Séminaire de probabilités de Strasbourg

Le comportement de dernière sortie

Bernard Maisonneuve (1975)

Séminaire de probabilités de Strasbourg

Le principe du maximum et l'hypoellipticité globale

K. Taira (1984/1985)

Séminaire Équations aux dérivées partielles (Polytechnique)

Le théorème de Ray-Knight à temps fixe

Christophe Leuridan (1998)

Séminaire de probabilités de Strasbourg

Lectures on Logarithmic Sobolev Inequalities

A. Guionnet, B. Zegarlinski (2002)

Séminaire de probabilités de Strasbourg

Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group

David Applebaum, Serge Cohen (2004)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Limit theorems for stationary Markov processes with L2-spectral gap

Déborah Ferré, Loïc Hervé, James Ledoux (2012)

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

Let ${(X_{t}, Y_{t})}_{t \in 𝕋}$ be a discrete or continuous-time Markov process with state space $𝕏 \times ℝ^{d}$ where $𝕏$ is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. ${(X_{t}, Y_{t})}_{t \in 𝕋}$ is assumed to be a Markov additive process. In particular, this implies that the first component ${(X_{t})}_{t \in 𝕋}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process ${(Y_{t})}_{t \in 𝕋}$ is shown to satisfy the...

Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX

Bernard Roynette, Marc Yor (2010)

ESAIM: Probability and Statistics

We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional: $(A_{t}^{-} : = \int_{0}^{t} 1_{X_{s} < 0} d s, t \geq 0)$ . On the other hand, we describe Feynman-Kac type penalisation results for long Brownian bridges thus completing some similar previous study for standard Brownian motion (see [B. Roynette, P. Vallois and M. Yor, Studia Sci. Math. Hung.43 (2006) 171–246]).