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.
Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in with non-zero mean.
Existence of moments of increasing predictable processes associated with one- and two-parameter potentials.
Existence of nontrivial stochastic monoids.
Existence of positive harmonic functions on groups and on covering manifolds
Existence, uniqueness and regularity of parabolic SPDEs driven by Poisson random measure.
Expansion and random walks in : I
We prove that the Cayley graphs of are expanders with respect to the projection of any fixed elements in generating a Zariski dense subgroup.
Expansion and random walks in : II
Expansions for Gaussian processes and Parseval frames.
Expectation, conditional expectation and martingales in local fields.
Expected number of real zeros of Lévy and harmonizable stable random polynomials.
Explicit Karhunen-Loève expansions related to the Green function of the Laplacian
Karhunen-Loève expansions of Gaussian processes have numerous applications in Probability and Statistics. Unfortunately the set of Gaussian processes with explicitly known spectrum and eigenfunctions is narrow. An interpretation of three historical examples enables us to understand the key role of the Laplacian. This allows us to extend the set of Gaussian processes for which a very explicit Karhunen-Loève expansion can be derived.
Explicit solutions of some fractional partial differential equations via stable subordinators.
Explosion time in stochastic differential equations with small diffusion.
Exponential approximation for hitting times in mixing processes.