Eventual intersection for sequences of Lévy processes.
Every continuous first order autoregressive stochastic process is a Gaussian process
Exact rate of convergence for increments of random fields.
Exact rates in Vapnik-Chervonenkis bounds
Exact representations for tumour incidence for some density-dependent models.
Example of continuous second-order stochastic process with prescribed finite multiplicity
Examples and counterexamples to almost-sure convergence of bilateral martingales.
Examples of convergence and non-convergence of Markov chains conditioned not to die.
Examples on local martingales
Exchangeable fragmentation-coalescence processes and their equilibrium measures.
Exchangeable measures for subshifts
Exchanging the order of taking suprema and countable intersections of σ-algebras
Excited against the tide: a random walk with competing drifts
We study excited random walks in i.i.d. random cookie environments in high dimensions, where the th cookie at a site determines the transition probabilities (to the left and right) for the th departure from that site. We show that in high dimensions, when the expected right drift of the first cookie is sufficiently large, the velocity is strictly positive, regardless of the strengths and signs of subsequent cookies. Under additional conditions on the cookie environment, we show that the limiting...
Excited random walk.
Excited random walk on trees.
Excursions of the integral of the brownian motion
The integrated brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a stationary Langevin process and then determine explicitly its stationary excursion measure. This is then used to provide new descriptions of Itô’s excursion measure of the Langevin process reflected at a completely inelastic boundary, which has been...
Existence and asymptotic behaviour of some time-inhomogeneous diffusions
Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters , and , of the recurrence, transience and convergence. More precisely, asymptotic...
Existence and simulation of Gibbs-Delaunay-Laguerre tessellations
Three-dimensional Laguerre tessellation models became quite popular in many areas of physics and biology. They are generated by locally finite configurations of marked points. Randomness is included by assuming that the set of generators is formed by a marked point process. The present paper focuses on 3D marked Gibbs point processes of generators which enable us to specify the desired geometry of the Laguerre tessellation. In order to prove the existence of a stationary Gibbs measure using a general...
Existence de processus Markoviens pour des systèmes infinis de particules
Existence et régularité höldérienne des fonctions de bosses
We discuss the almost sure existence of random functions that can be written as sums of elementary pulses. We then estimate their uniform Hölder regularity by applying some results on coverings by random intervals.