PATHWISE DECOMPOSITIONS OF BROWNIAN SEMISTATIONARY PROCESSES.

We find a pathwise decomposition of a certain class of Brownian semistationary processes (BSS) in terms of fractional Brownian motions. To do this, we specialize in the case when the kernel of the BSS is given by ϕα(x) = L(x)xα with α ∈ (-1/2, 0) ∪ (0, 1/2) and L a continuous function slowly varying at zero. We use this decomposition to study some path properties and derive Itˆo's formula for this subclass of BSS processes. [ABSTRACT FROM AUTHOR]