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

In this paper, we study higher order variations of iterated Brownian motion (IBM) with view towards possible applications to the construction of the stochastic integral with respect to IBM. We prove that the 4-th variation of IBM is a deterministic linear function. This clearly means that the quadratic variation is infinite ...

Let D be the Wiener sausage of width [epsilon] around two-sided Brownian motion. The components of two-dimensional reflected Brownian motion in D converge to one-dimensional Brownian motion and iterated Brownian motion, resp., as [epsilon] goes to 0.

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.