Exact transient expectations for queueing networks
Exact transient solution of a state-dependent birth-death process.
Example of continuous second-order stochastic process with prescribed finite multiplicity
Examples and counterexamples to almost-sure convergence of bilateral martingales.
Examples of condition for diffusions in a random environment.
Examples of convergence and non-convergence of Markov chains conditioned not to die.
Examples on local martingales
Excercises in stochastic analysis
Exchangeable fragmentation-coalescence processes and their equilibrium measures.
Exchangeable measures for subshifts
Exchangeable pairs and Poisson approximation.
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.
Excursion laws and exceptional points on brownian paths
Excursions into a new duality relation for diffusion processes.
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...
Exemples de théorèmes locaux sur les groupes résolubles