Brownian Excursions and Minimal Thinness. Part III: Applications to the Angular Derivative Problem.
Brownian excursions from extremes
Brownian excursions, stochastic integrals, and representation of Wiener functionals.
Brownian filtrations are not stable under equivalent time-changes
Brownian local minima, random dense countable sets and random equivalence classes.
Brownian local times.
Brownian local times and branching processes
Brownian Motion and Eigenvalues for the Dirichlet Laplacian.
Brownian motion and generalized analytic and inner functions
Let be a mapping from an open set in into , with . To say that preserves Brownian motion, up to a random change of clock, means that is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case , , such conditions signify that corresponds to an analytic function of one complex variable. We study, essentially that case , , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for , would solve...
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
Brownian motion and random obstacles.
Brownian motion and random walks on manifolds
We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.
Brownian motion and stereographic projection
Brownian motion and transient groups
In this paper I consider a covering of a Riemannian manifold . I prove that Green’s function exists on if any and only if the symmetric translation invariant random walks on the covering group are transient (under the assumption that is compact).
Brownian motion, approximation of functions, and Fourier analysis
Brownian motion, bridge excursion, and meander characterized by sampling at independent uniform times.
Brownian motion, excursions, and matrix factors
Brownian motion in a Poisson obstacle field
Brownian motion in a Weyl chamber, non-colliding particles, and random matrices
Brownian motion on a surface of negative curvature