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Displaying 21 – 25 of 25

Lipschitzian norm estimate of one-dimensional Poisson equations and applications

Hacene Djellout, Liming Wu (2011)

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

By direct calculus we identify explicitly the lipschitzian norm of the solution of the Poisson equation in terms of various norms of g, where is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the L1-Poincaré inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several illustrative...

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]).

Local property of Dirichlet forms and diffusions on general state spaces.

S. Albeverio, Z.M Ma, M. Röckner (1993)

Mathematische Annalen

Logarithmic Sobolev inequalities for inhomogeneous Markov Semigroups

Jean-François Collet, Florent Malrieu (2008)

ESAIM: Probability and Statistics

We investigate the dissipativity properties of a class of scalar second order parabolic partial differential equations with time-dependent coefficients. We provide explicit condition on the drift term which ensure that the relative entropy of one particular orbit with respect to some other one decreases to zero. The decay rate is obtained explicitly by the use of a Sobolev logarithmic inequality for the associated semigroup, which is derived by an adaptation of Bakry's Γ-calculus. As a byproduct,...

Long time behaviour and stationary regime of memory gradient diffusions

Sébastien Gadat, Fabien Panloup (2014)

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

In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for the long-time stability of the dynamical system and then provide, when stable, some convergence properties of the occupation measures and of the...

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