On a construction of Markov processes associated with time dependent Dirichlet spaces.
On a theorem of Cartan
On exit laws for semigroups in weak duality
Let be a measurable semigroup and a -finite positive measure on a Lusin space . An -exit law for is a family of nonnegative measurable functions on which are finite -a.e. and satisfy for each
On harmonic functions of symmetric Lévy processes
We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in (Potential Anal.17 (2002) 375–388)) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Hölder continuity estimates of harmonic functions. Despite the failure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from (Probab. Theory Related Fields135 (2006) 547–575) and obtain asymptotic...
On (r, 2)-capacities for a class of elliptic pseudo differential operators.
On reflecting brownian motion — a weak convergence approach
On semi-martingale characterizations of functionals of symmetric Markov processes.
On some properties of transition operators.
On strong Markov duals.
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