GAUSSIAN AND NON-GAUSSIAN PROCESSES OF ZERO POWER VARIATION

摘要

We consider a class of stochastic processes X defined by X (t) = integral(T)(0) G (t, s) dM (s) for t is an element of [0, T], where M is a square-integrable continuous martingale and G is a deterministic kernel. Let m be an odd integer. Under the assumption that the quadratic variation [M] of M is differentiable with E [vertical bar d [M] (t)/dt vertical bar(m)] finite, it is shown that the mth power variation