The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in C [to the power of gamma] domains, where [gamma](x) = bx log log(1/x)/ log log log(1/x), b small. A counterexample shows that this result is very nearly sharp.

Three-dimensional Brownian path reflected on Brownian path is a free Brownian path.

Our main results are (i) a new construction of reflected Brownian motion X in a half-plane with non-smooth angle of oblique reflection and (ii) a theorem on existence of some "exceptional" points on the paths of the standard two-dimensional Brownian motion. The link between these two seemingly disparate results will be formed ...

The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law.

Some examples are given of convex domains for which domain monotonicity of the Neumann heat kernel does not hold.

The present paper is devoted to studying path properties of iterated Brownian motion (IBM). We want to examine how the lack of independence of increments influences the results and estimates which are well understood in the Brownian case. This may be viewed as a prelude to a deeper study of the process.