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We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form $- ϵ Δ + \nabla F (\cdot) \nabla$ on $ℝ^{d}$ or subsets of $ℝ^{d}$ , where $F$ is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of $F$ can be related, up to multiplicative errors that tend to one as $ϵ ↓ 0$ , to the capacities of suitably constructed sets. We show that these capacities...

Metastability in reversible diffusion processes II: precise asymptotics for small eigenvalues

Anton Bovier, Véronique Gayrard, Markus Klein (2005)

Journal of the European Mathematical Society

We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form $- ϵ Δ + \nabla F (\cdot) \nabla$ on $ℝ^{d}$ or subsets of $ℝ^{d}$ , where $F$ is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum...

Minimal thinness for subordinate Brownian motion in half-space

Panki Kim, Renming Song, Zoran Vondraček (2012)

Annales de l’institut Fourier

We study minimal thinness in the half-space $H : = {x = (\tilde{x}, x_{d}) : \tilde{x} \in ℝ^{d - 1}, x_{d} > 0}$ for a large class of subordinate Brownian motions. We show that the same test for the minimal thinness of a subset of $H$ below the graph of a nonnegative Lipschitz function is valid for all processes in the considered class. In the classical case of Brownian motion this test was proved by Burdzy.

Minimization of the Kullback information for some Markov processes

Patrick Cattiaux, Christian Léonard (1996)

Séminaire de probabilités de Strasbourg

Minorantes harmoniques et potentiels - Localisation sur une famille de temps d'arrêt - Réduite forte

Hélène Airault (1974)

Annales de l'institut Fourier

$X = (X_{t}, ζ, M_{t}, E_{x})$ est un processus de Markov sur un espace localement compact, et $h$ est une fonction excessive. Soit $T$ une famille de temps d’arrêt $h$ est $T$ -harmonique si pour tout $x$ , $E_{x} [h (X_{t})] = h (x)$ pour tout temps d’arrêt $τ$ appartenant à $T$ . $h$ est un $T$ potentiel si sa plus grande minorante forte $T$ -harmonique est nulle. La plus grande minorante forte $T$ -harmonique de $h$ est égale à la somme de deux fonctions excessives qui sont étudiées. On déduit différentes caractérisations des $T$ -potentiels suivant les propriétés de la famille...

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Displaying 1 – 15 of 15

Marches de Harris sur les groupes localement compacts. II

Markov functions

Markov Processes with Identiacl Hitting Probalities.

Markov Processes with Identical Excessive Measures.

Martingales et changement de temps

Measures charging no polar sets and additive functional of Brownian motion.

Measures of finite (r,p)-energy and potentials on a separable metric space

Metastability in reversible diffusion processes I: Sharp asymptotics for capacities and exit times

Metastability in reversible diffusion processes II: precise asymptotics for small eigenvalues

Minimal thinness for subordinate Brownian motion in half-space

Minimization of the Kullback information for some Markov processes

Minorantes harmoniques et potentiels - Localisation sur une famille de temps d'arrêt - Réduite forte

More on existence and uniqueness of decomposition of excessive functions and measures into extremes

Multiplicative excessive measures and duality between equations of Boltzmann and of branching processes

Multiplicities of a random sausage

Currently displaying 1 – 15 of 15