On the ergodic distribution of oscillating queueing systems.
On the existence of a dual semigroup
On the existence of recurrent extensions of self-similar Markov processes.
On the Poisson equation in the potential theory of a single kernel.
On the Potential Theory of Symmetric Markov Porcesses.
On the probabilistic multichain Poisson equation
This paper introduces necessary and/or sufficient conditions for the existence of solutions (g,h) to the probabilistic multichain Poisson equation (a) g = Pg and (b) g+h-Ph = f, with a given charge f, where P is a Markov kernel (or transition probability function) on a general measurable space. The existence conditions are derived via three different approaches, using (1) canonical pairs, (2) Cesàro averages, and (3) resolvents.
On the Ray topology
On the separately excessive functions. (Sur les fonctions séparément excessives.)
On the structure of subordinate semigroups.
On the volume of intersection of three independent Wiener sausages
Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.
On Veech's conjecture for harmonic functions
One-dimensional potential embedding
One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization
Opérateurs potentiels des chaînes et des processus de Markov irréductibles
Parabolic Harnack inequality and estimates of Markov chains on graphs.
On a graph, we give a characterization of a parabolic Harnack inequality and Gaussian estimates for reversible Markov chains by geometric properties (volume regularity and Poincaré inequality).
Penetration times and Skorohod stopping
Permanent sets of measures charging no exceptional sets and the Feynman-Kac Formula.
Pitman's theorem for skip-free random walks with Markovian increments.
Poisson kernel and Green function of balls for complex hyperbolic Brownian motion
The aim of this paper is to give a description of the Poisson kernel and the Green function of balls in the complex hyperbolic space. The description is in terms of the hypergeometric function and unitary spherical harmonics in ℂⁿ.
Poisson kernels of half-spaces in real hyperbolic spaces.