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Keywords and phrases: Transition Densities, Brownian Motion, Eigenvalue Expansion, Fine Topology, Regular
(2007) use ingenious arguments based on ideas from differential games to show that a bounded convex planar domain cannot support any shy couplings of reflected Brownian motions if
One of the purposes of this paper is to point out that there exists an eigenvalue expansion for the transition densities of Brownian motion killed on exiting an arbitrary Borel subset
Indeed, it seems that case (a) should give us the right picture: in the limit, in between large events lineages perform Brownian motions on the torus of sidelength 1 due to
We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position.. The derivative is a linear
Key words: Brownian areas, asymptotics for density functions right tail, double Laplace transform, two-dimensional saddle point method.. AMS 2000 Subject Classification:
When X and Y are Brownian motions on a Riemannian manifold, Kendall [3] and Cranston [1] constructed a coupling by using the Riemannian geometry of the underlying space.. Their
In the present paper we construct such a Hermitian matrix-valued process, whose entries are sums of Brownian motions and Brownian bridges given independently of each other, that
