A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion.
A central limit theorem for two-dimensional random walks in a cone
We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only if the tail distribution of the exit time from the cone is regularly varying. This condition is satisfied in many natural examples.
A characterization of BMO and
A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations translations and dilatations
The exit distribution for open sets of a path-continuous, strong Markov process in is characterized as a weak star limit of successive spherical sweepings of measures, starting with the unit point mass. Then this is used to prove that two path-continuous strong Markov processes with identical exit distributions from balls when starting form the center, have identical exit distributions from all opens sets, provided they both exit a.s. from bounded sets. This implies that the only path-continuous,...
A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces
denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on is harmonic if and only if it is the projection of a measure on the unit tangent bundle of which is invariant under both the geodesic and the horocycle flows.
A conservative evolution of the Brownian excursion.
A counterexample for the optimality of Kendall-Cranston coupling.
A critical function for the planar brownian convex hull
A family of integral representations for the brownian variables
A Gaussian correlation inequality and its applications to small ball probabilities.
A gaussian sheet connected to symmetric Markov chains
A large Wiener sausage from crumbs.
A martingale approach to some Wiener-Hopf problems, I
A martingale approach to some Wiener-Hopf problems, II
A martingale proof of the Khinchin iterated logarithm law for Wiener processes
A metric property of some random functions
A multiplier characterization of analytic UMD spaces
A non-reversible semi-martingale
A note on a.s. finiteness of perpetual integral functionals of diffusions.
A note on large deviations for Wiener chaos