Let (Xt)t[greater-or-equal, slanted]0 be a non-singular (not necessarily recurrent) diffusion on starting at zero, and let [nu] be a probability measure on Necessary and sufficient conditions are established for [nu] to admit the existence of a stopping time [tau]* of (Xt) solving the Skorokhod...

In this paper, we establish the moderate deviations for occupation times of Markov processes under the conditions given in Darling-Kac (1957. Trans. Amer. Math. Soc. 84, 444-458). When applied to the law of the iterated logarithm, our results generalize those obtained in Marcus-Rosen (1994a....

New rates of convergence in the multidimensional functional CLT are given by means of the Prokhorov's distance between a brownian motion and a continuous time martingale, with no further assumption than square integrability. The results are completely and simply expressed with distances of...

In this article we prove new results concerning the structure and the stability properties of the global attractor associated with a class of nonlinear stochastic partial differential equations driven by finite-dimensional Wiener processes. This class encompasses important equations that occur...

We establish the rate of growth of the length of long strange intervals in an infinite moving average process whose coefficients are regularly varying at infinity. We compute the limiting distribution of the appropriately normalized length of such intervals. The rate of growth of the length of...

We study relations between P{supt[set membership, variant][0,h] [xi](t)>u} and for a stationary process [xi](t). Applications include Markov jump processes, [alpha]-stable processes, and quadratic functionals of Gaussian processes.

We obtain in this paper moderate deviations for functional empirical processes of general state space valued Markov chains with atom under weak conditions: a tail condition on the first time of return to the atom, and usual conditions on the class of functions. Our proofs rely on the...

We study polling systems with Poisson arrival streams and exhaustive service discipline in the critical load case [rho]=1. We show that the system may exhibit null-recurrence or transient behavior and give the corresponding conditions in terms of the first two moments of the distribution of...

In this paper, we study the two-sided taboo limit processes that arise when a Markov chain or process is conditioned on staying in some set A for a long period of time. The taboo limit is time-homogeneous after time 0 and time-inhomogeneous before time 0. The time-reversed limit has this same...