On the joining of sticky brownian motion
On the Lévy transformation of brownian motions and continuous martingales
On the maximum of a diffusion process in a drifted brownian environment
On the noncoalescence of a two point brownian motion reflecting on a circle
On the occupation time of Brownian excursion.
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 relative lengths of excursions derived from a stable subordinator
On the sample path behavior of the first passage time process of a brownian motion with drift
On the self-intersection local time of Brownian motion via chaos expansion.
On the sojourn times of killed brownian motion
On the space of vector-valued functions integrable with respect to the white noise
On the Spitzer and Chung laws of the iterated logarithm for brownian motion
On the sum of two Brownian paths
On the time of the maximum of Brownian motion with drift.
On the upcrossing chains of stopped brownian motion
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 Walsh's brownian motions
On weak brownian motions of arbitrary order
Opérateur de Schrödinger à résolvante compacte