Théorème central-limite pour le groupe des déplacements de
Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples.
On ℝd-valued peacocks
In this paper, we consider ℝ-valued integrable processes which are increasing in the convex order, ℝ-valued peacocks in our terminology. After the presentation of some examples, we show that an ℝ-valued process is a peacock if and only if it has the same one-dimensional marginals as an ℝ-valued martingale. This extends former results, obtained notably by Strassen [36 (1965) 423–439], Doob [2 (1968) 207–225] and Kellerer [198 (1972) 99–122].
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX
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: . 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, (2006) 171–246]).
Un théorème de Schilder pour des fonctionnelles browniennes non régulières
On long time almost sure asymptotics of renormalized branching diffusion processes
Recollement de deux processus de Markov et fonctionnelles additives
Retournement des processus de Markov à un temps fixe. Remarque sur l'hypothèse de dualité
Couples de Wald indéfiniment divisibles. Exemples liés à la fonction gamma d'Euler et à la fonction zeta de Riemann
A toute mesure positive sur telle que , nous associons un couple de Wald indéfiniment divisible, i.e. un couple de variables aléatoires tel que et sont indéfiniment divisibles, , et pour tout . Plus généralement, à une mesure positive sur telle que pour tout , nous associons une “famille d’Esscher” de couples de Wald indéfiniment divisibles. Nous donnons de nombreux exemples de telles familles d’Esscher. Celles liées à la fonction gamma et à la fonction zeta de Riemann possèdent...
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes
Let be a Lévy process started at , with Lévy measure . We consider the first passage time of to level , and the overshoot and the undershoot. We first prove that the Laplace transform of the random triple satisfies some kind of integral equation. Second, assuming that admits exponential moments, we show that converges in distribution as , where denotes a suitable renormalization of .
A singular large deviations phenomenon
Branching process associated with 2d-Navier Stokes equation.
Ω being a bounded open set in R, with regular boundary, we associate with Navier-Stokes equation in Ω where the velocity is null on ∂Ω, a non-linear branching process (Y, t ≥ 0). More precisely: E(〈h,Y〉) = 〈ω,h〉, for any test function h, where ω = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Y increases or decreases in one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation of vortex...
Independence of time and position for a random walk.
Penalisations of multidimensional Brownian motion, VI
As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals Γ, we obtain here the existence of the limit, as → ∞, of -dimensional Wiener measures penalized by a function of the maximum up to time of the Brownian winding process (for ), or in 2 dimensions for Brownian motion prevented to exit a cone before time . Various extensions of these multidimensional penalisations are studied, and the limit laws are described....
Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes
Let () be a Lévy process started at , with Lévy measure . We consider the first passage time of () to level , and the overshoot and the undershoot. We first prove that the Laplace transform of the random triple () satisfies some kind of integral equation. Second, assuming that admits exponential moments, we show that converges in distribution as → ∞, where denotes a suitable renormalization of .
Abel transform and integrals of Bessel local times
Processus de Markov : retournement des trajectoires à un temps d'entrée dans un presque-borélien
On independent times and positions for Brownian motions.
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