On the occupation measure of super-Brownian motion.
On the occupation time of Brownian excursion.
On the Onsager-Machlup functional for elliptic diffusion processes
On the parabolic generator of a general one-dimensional Lev́y process.
On the perturbation of Markov chains with nearly transient states.
On the Poisson equation in the potential theory of a single kernel.
On the Potential Theory of Symmetric Markov Porcesses.
On the principle of smooth fit for killed diffusions.
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 Range of the Generator of a Markovian Semigroup.
On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed mixing...
On the rate of growth of subordinators with slowly varying Laplace exponent
On the Ray topology
On the reconstruction of a killed Markov process
On the regularity of stochastic currents, fractional brownian motion and applications to a turbulence model
We study the pathwise regularity of the map φ↦I(φ)=∫0T〈φ(Xt), dXt〉, where φ is a vector function on ℝd belonging to some Banach space V, X is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A continuous version of this map, seen as a random element of the topological dual of V will be called stochastic current. We give sufficient conditions for the current to live in some Sobolev space of distributions and we provide elements to conjecture...
On the relation between elliptic and parabolic Harnack inequalities
We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suffices to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suffices to imply the parabolic Harnack inequality in question; both are necessary conditions. As an application, we show the equivalence between parabolic Harnack inequality for on , (i.e., for ) and elliptic Harnack inequality for on .
On the relationship between subordinate killed and killed subordinate processes.
On the relative lengths of excursions derived from a stable subordinator
On the re-rooting invariance property of Lev́y trees.
On the sample path behavior of the first passage time process of a brownian motion with drift