We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4.

An asymptotically 4-stable process is constructed. The model identifies the 4-stable process with a sequence of processes converging in a very weak sense. It is proved that the 4-th variation of the process is a linear function of time and its quadratic variation may be identified with a Brownian motion.

We consider two-dimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded variation away from the tip of the thorn. The construction is based on a new Skorohod-type lemma.

We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains.

Suppose that X is a two-dimensional Brownian motion. The trace X[0, 1] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.

Suppose [epsilon] [is a member of the set] [0, 1) and let theta [subscipt epsilon] (t) = (1 − [epsilon]) [square root of] (2tln [subscript] 2 t). Let L [to the power of epsilon] [subscript] t denote the amount of local time spent by Brownian motion on the curve [theta subscript epsilon] (s) before time t. If [epsilon] > 0 ...