Gaussian and non-Gaussian processes of zero power variation

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This paper considers the class of stochastic processes X defined on [0, T] by X (t) = R T 0 G(t, s) dM (s) where M is a square-integrable martingale and G is a deterministic kernel. When M is Brownian motion, X is Gaussian, and the class includes fractional Brownian motion and other Gaussian processes with or without homogeneous increments. Let m be an odd integer. Under the asumption that the quadratic variation [M] of M is differentiable with E[|d[M] /dt| m ] finite, it is shown that the mth power variation