The calculus of boundary processes
The chance of a long lifetime for Brownian motion in a horn-shaped domain.
The compact support property for measure-valued processes
The evolution and Poisson kernels on nilpotent meta-abelian groups
Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to , k>1. We consider a class of second order left-invariant differential operators on S of the form , where , and for each is left-invariant second order differential operator on N and , where Δ is the usual Laplacian on . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...
The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane
The gap between the past supremum and the future infimum of a transient Bessel process
The heat equation on manifolds as a gradient flow in the Wasserstein space
We study the gradient flow for the relative entropy functional on probability measures over a riemannian manifold. To this aim we present a notion of a riemannian structure on the Wasserstein space. If the Ricci curvature is bounded below we establish existence and contractivity of the gradient flow using a discrete approximation scheme. Furthermore we show that its trajectories coincide with solutions to the heat equation.
The hypercontractivity of Ornstein-Uhlenbeck semigroups with drift, revisited
The infinite Brownian loop on a symmetric space.
The Kolmogorov equation with time-measurable coefficients.
The law of the maximum of a Bessel bridge.
The Lenz shift and wiener sausage in riemannian manifolds
The lifetimes of conditioned diffusion processes
The "local" law of the iterated logarithm for processes related to Lévy's stochastic area process
The -Wright function in time-fractional diffusion processes: a tutorial survey.
The moments of the area under reflected Brownian bridge conditional on its local time at zero.
The noise made by a Poisson snake.
The renormalization transformation for two-type branching models
This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting within colonies. Their large-scale space–time behavior can be studied by means of a renormalization program. This program, which has been carried out successfully in a number of other cases (mostly one-dimensional), is based on the construction and the analysis of...
The “Riemann hypothesis” for the Hawkins random Sieve
The Skorokhod oblique reflection problem in a convex polyhedron.