Exact mixing in an unknown Markov chain.
Exact rates of convergence to the local times of symmetric Lévy processes
Exact solution of the Bellman equation for a -discounted reward in a two-armed bandit with switching arms.
Exact transient solution of a state-dependent birth-death process.
Examples of convergence and non-convergence of Markov chains conditioned not to die.
Exchangeable fragmentation-coalescence processes and their equilibrium measures.
Excited random walk on trees.
Excursion laws and exceptional points on brownian paths
Excursions of diffusion processes and continued fractions
It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.
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 uniqueness of diffusions on finitely ramified self-similar fractals
Existence de processus Markoviens pour des systèmes infinis de particules
Existence et unicité de diffusions à valeurs dans un espace de Hilbert
Existence of graphs with sub exponential transitions probability decay and applications
In this paper, we recall the existence of graphs with bounded valency such that the simple random walk has a return probability at time at the origin of order for fixed and with Følner function . This result was proved by Erschler (see [4], [3]); we give a more detailed proof of this construction in the appendix. In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random walk on...
Existence of moments of increasing predictable processes associated with one- and two-parameter potentials.
Existence of positive harmonic functions on groups and on covering manifolds
Existence of small oscillations at zeros of brownian motion
Exit time, Green function and semilinear elliptic equations.
Exit times of symmetric stable processes from unbounded convex domains.